Module ising_animate.ising
Expand source code
from math import exp, sin
import matplotlib.pyplot as plt
from matplotlib.animation import FuncAnimation
from matplotlib.colors import Normalize
from matplotlib.ticker import StrMethodFormatter
from .lattice import Lattice
plt.rcParams.update({"figure.autolayout": True})
class Ising:
"""
The core implementation of the Ising Model. No animation here.
Args
------------------
shape : 2-tuple of ints; Default is (128, 128)
the shape of the lattice of spins.
temp : float; Default is 2.0
the initial temperature of the lattice as a whole.
j : float or 2-tuple of floats; Default is 1.0
the coefficient of interaction between neighboring spins in the lattice.
when a tuple is suplied, the first value is the coefficient for row neighbors
and the second value is the coefficient for column neighbors.
field : float; Default is 0.0
the initial value for the external magnetic field.
init_state : {"random", "down", "up"}; Default is "random"
the initial configuration of the spins in the lattice.
Attributes
------------------
gen : int
the current generation of the system. Starts at 0 and is
incremented by a call to update method
init_state : {"random", "down", "up"}; Default is "random"
the initial configuration of the spins in the lattice.
spins : int
the number of the spins in the lattice
lattice : Lattice
an instance of a Lattice object that describes the
current state of the system
temp : float
the current temperature of the lattice, in energy units.
A new value can be assigned anytime.
field : float
the current value of the external magnetic field, oriented
perpendicularlly to the lattice. A positive value represents
a up oriented field. A new value can be assigned anytime.
energy : float
the total energy of the lattice in its current generation.
mag_mom : float
the total magnetic moment of the lattice in its current generation.
mean_energy_hist : list[float]
a list with the values of the mean energy for each past generation.
New values are appended by a call to the update function
magnet_hist : list[float]
a list with the values of the magnetization per spin
for each past generation. New values are appended by a call to
the update function
specific_heat_hist : list[float]
a list with the values of the specific heat per spin
for each past generation. New values are appended by a call to
the update function
susceptibility_hist : list[float]
a list with the values of the magnetic susceptibility
for each past generation. New values are appended by a call to
the update function
"""
def __init__(
self,
shape=(128, 128),
temp=2.0,
j=(1.0, 1.0),
field=0.0,
init_state="random",
) -> None:
# Saving given init_state to include in __str__
if init_state == "up":
self._init_state = "up"
elif init_state == "down":
self._init_state = "down"
else:
self._init_state = "random"
self.lattice = Lattice(shape, temp, j, field, init_state)
self._energy = self.lattice.energy
self._mag_mom = self.lattice.mag_mom
self.mean_energy_hist = [self.lattice.mean_energy()]
self.magnet_hist = [self.lattice.magnet() / self.spins]
self.specific_heat_hist = [0.0]
self.susceptibility_hist = [0.0]
def __repr__(self) -> str:
return (
f"Ising(shape={self.lattice.shape.__str__()}, "
+ f"temp={self.lattice.temp}, "
+ f"j={self.lattice.j.__str__()}, "
+ f"field={self.lattice.field})"
)
def __str__(self) -> str:
return (
f"Ising Model with Temperature {self.lattice.temp:.2f} and Field {self.lattice.field:.2f}, "
+ f"starting with {self.init_state} spins"
)
@property
def spins(self):
return self.lattice.spins
@property
def init_state(self):
return self._init_state
@property
def gen(self):
return self.lattice._gen
@property
def temp(self):
return self.lattice.temp
@temp.setter
def temp(self, value):
self.lattice.temp = value
@property
def field(self):
return self.lattice.field
@field.setter
def field(self, value):
self.lattice.field = value
@property
def energy(self):
return self.lattice.energy
@property
def mag_mom(self):
return self.lattice.mag_mom
def update(self):
"""
Updates the system to the next generation, appending new values to
the history list of each phisical quantity.
"""
self.lattice.update()
self.mean_energy_hist.append(self.lattice.mean_energy())
self.magnet_hist.append(self.lattice.magnet() / self.spins)
self.specific_heat_hist.append(self.lattice.specific_heat() / self.spins)
self.susceptibility_hist.append(self.lattice.susceptibility())
class AnimatedIsing(Ising):
"""
Animation of the Ising Model at constant temperature and
constant external magnetic field
Args
------------------
shape : 2-tuple of ints. Default is (128, 128)
the shape of the lattice of spins.
temp : float. Default is 2.0
the initial temperature of the lattice as a whole.
j : float or 2-tuple of floats. Default is 1.0
the coefficient of interaction between neighboring spins in the lattice.
when a tuple is suplied, the first value is the coefficient for row neighbors
and the second value is the coefficient for column neighbors.
field : float. Default is 0.0
the initial value for the external magnetic field.
init_state : {"random", "down", "up"}. Default is "random"
the initial configuration of the spins in the lattice.
time_series : bool. Default is False
wheater or not to include the time series of the macroscopic
physical quantities in the animation
interval : int. Default is 100
the interval between each frame in the animation, in milliseconds
frames : int. Default is 60
the number of frames to include in the animation
Attributes
------------------
gen : int
the current generation of the system. Starts at 0 and is
incremented by a call to update method
interval : int
the interval between each frame in the animation, in milliseconds
frames : int.
the number of frames to include in the animation
time : float
elapsed time, considering one update per frame
init_state : {"random", "down", "up"}; Default is "random"
the initial configuration of the spins in the lattice.
spins : int
the number of the spins in the lattice
lattice : Lattice
an instance of a Lattice object that describes the
current state of the system
animation : FuncAnimation
a matplotlib.animation.FuncAnimation object. The animation is saved
with a call to animation.save("outfile.gif"). More info at
https://matplotlib.org/stable/api/_as_gen/matplotlib.animation.FuncAnimation.html
fig : Figure
a matplotlib.figure.Figure object in which the animation takes place. More info at
https://matplotlib.org/stable/api/figure_api.html?highlight=figure#matplotlib.figure.Figure
ax : Axes or list of Axes
single instance or list of matplotlib.axes.Axes objects. This are the axes in the
figures in the animation. More info at
https://matplotlib.org/stable/api/axes_api.html?highlight=axes#module-matplotlib.axes
temp : float
the current temperature of the lattice, in energy units.
A new value can be assigned anytime.
field : float
the current value of the external magnetic field, oriented
perpendicularlly to the lattice. A positive value represents
a up oriented field. A new value can be assigned anytime.
energy : float
the total energy of the lattice in its current generation.
mag_mom : float
the total magnetic moment of the lattice in its current generation.
time_hist : list[float]
a list with the values of time for each past generation.
New values are appended by a call to the update function
mean_energy_hist : list[float]
a list with the values of the mean energy for each past generation.
New values are appended by a call to the update function
magnet_hist : list[float]
a list with the values of the magnetization per spin
for each past generation. New values are appended by a call to
the update function
specific_heat_hist : list[float]
a list with the values of the specific heat per spin
for each past generation. New values are appended by a call to
the update function
susceptibility_hist : list[float]
a list with the values of the magnetic susceptibility
for each past generation. New values are appended by a call to
the update function
"""
def __init__(
self,
shape=(128, 128),
temp=2,
j=(1, 1),
field=0,
init_state="random",
time_series=False,
interval=100,
frames=60,
) -> None:
super().__init__(
shape=shape,
temp=temp,
j=j,
field=field,
init_state=init_state,
)
self.time_series = bool(time_series)
if self.time_series:
self.fig, self.ax = plt.subplots(3, 2)
self.fig.set_size_inches(10.8, 7.2)
# Merging axis [0, 0] and [1, 0]
gridspec = self.ax[0, 0].get_gridspec()
for ax in self.ax[0:2, 0]:
ax.remove()
self.fig.add_subplot(gridspec[0:2, 0])
self.ax = self.fig.get_axes() # ax[0, 0] is now ax[4]
self.ax.insert(0, self.ax.pop()) # ax[4] is now ax[0]
self.__update_animation = self.__update_ani_time_series
self.__init_animation = self.__init_ani_time_series
else:
self.fig, self.ax = plt.subplots()
self.fig.set_size_inches(7.2, 4.8)
self.__update_animation = self.__update_ani_no_time_series
self.__init_animation = self.__init_ani_no_time_series
self.fig.suptitle(self.__str__())
self.interval = interval
self.frames = frames
self.time_hist = [self.time]
self.animation = FuncAnimation(
self.fig,
func=self.__update_animation,
init_func=self.__init_animation,
interval=self.interval,
save_count=self.frames,
)
self.axes_labels = {
"time": r"$t$",
"energy": r"$\langle E \rangle$",
"magnet": r"$\langle \mu \rangle / n$",
"specific_heat": r"$C / n$",
"susceptibility": r"$\chi$",
}
def __repr__(self) -> str:
return (
f"AnimatedIsing(shape={self.lattice.shape.__str__()}, "
+ f"temp={self.lattice.temp}, "
+ f"j={self.lattice.j.__str__()}, "
+ f"field={self.lattice.field}, "
+ f"time_series={self.time_series}, "
+ f"interval={self.interval}, "
+ f"frames={self.frames})"
)
@property
def time(self):
return self.gen * self.interval / 1000
def update(self):
"""
Updates the system to the next generation, appending new values to
the history list of each phisical quantity. This function is automatically
called by the animation attribute to render the next frame.
"""
super().update()
self.time_hist.append(self.time)
def __set_axes(self):
for ax in self.ax[1:]:
ax.yaxis.set_major_formatter(StrMethodFormatter("{x:.1e}"))
ax.set(
xlim=(0, self.frames * self.interval / 1000),
xlabel=self.axes_labels["time"],
)
ax.grid(linestyle=":")
self.ax[0].set(ylabel="i", xlabel="j")
self.ax[1].set(ylabel=self.axes_labels["energy"])
self.ax[2].set(ylabel=self.axes_labels["magnet"])
self.ax[3].set(ylabel=self.axes_labels["specific_heat"])
self.ax[4].set(ylabel=self.axes_labels["susceptibility"])
def __init_ani_time_series(self):
self.__set_axes()
self.ax[0].imshow(self.lattice.state, norm=Normalize(vmin=-1.0, vmax=1.0))
def __update_ani_time_series(self, frame):
for ax in self.ax:
ax.clear()
self.update()
self.__set_axes()
self.fig.suptitle(self.__str__())
self.ax[0].imshow(self.lattice.state, norm=Normalize(vmin=-1.0, vmax=1.0))
self.ax[1].plot(self.time_hist, self.mean_energy_hist, color="purple")
self.ax[2].plot(self.time_hist, self.magnet_hist, color="purple")
self.ax[3].plot(self.time_hist, self.specific_heat_hist, color="purple")
self.ax[4].plot(self.time_hist, self.susceptibility_hist, color="purple")
def __init_ani_no_time_series(self):
self.ax.set(ylabel="i", xlabel="j")
self.ax.imshow(self.lattice.state, norm=Normalize(vmin=-1.0, vmax=1.0))
def __update_ani_no_time_series(self, frame):
self.ax.clear()
self.update()
self.ax.set(ylabel="i", xlabel="j")
self.fig.suptitle(self.__str__())
self.ax.imshow(self.lattice.state, norm=Normalize(vmin=-1.0, vmax=1.0))
class CoolingAnimatedIsing(AnimatedIsing):
"""
Animation of the Ising Model at constant external magnetic field,
but with its temperature growing (or decaing) exponentially, given
initial and target values.
Args
------------------
shape : 2-tuple of ints
the shape of the lattice of spins. Default is (128, 128).
temp : float. Default is 5.0
the initial temperature of the lattice as a whole.
final_temp : float. Default is 1.0
the final temperature of the system.
cooling_rate : float. Default is 0.5
the rate with which the temperature will find its way to the final_temp.
(1 / cooling_rate) is the amount of time (in seconds) it takes to achieve about
63% of the way there.
j : float or 2-tuple of floats. Default is (1.0, 1.0)
the coefficient of interaction between neighboring spins in the lattice.
when a tuple is suplied, the first value is the coefficient for row neighbors
and the second value is the coefficient for column neighbors.
field : float. Default is 0.0
the initial value for the external magnetic field.
init_state : {"random", "down", "up"}. Default is "random"
the initial configuration of the spins in the lattice.
time_series : bool. Default is False
wheater or not to include the time series of the macroscopic
physical quantities in the animation
interval : int. Default is 100
the interval between each frame in the animation, in milliseconds
frames : int. Default is 60
the number of frames to include in the animation
Attributes
------------------
gen : int
the current generation of the system. Starts at 0 and is
incremented by a call to update method
init_state : {"random", "down", "up"}; Default is "random"
the initial configuration of the spins in the lattice.
spins : int
the number of the spins in the lattice
lattice : Lattice
an instance of a Lattice object that describes the
current state of the system
animation : FuncAnimation
a matplotlib.animation.FuncAnimation object. The animation is saved
with a call to animation.save("outfile.gif"). More info at
https://matplotlib.org/stable/api/_as_gen/matplotlib.animation.FuncAnimation.html
fig : Figure
a matplotlib.figure.Figure object in which the animation takes place. More info at
https://matplotlib.org/stable/api/figure_api.html?highlight=figure#matplotlib.figure.Figure
ax : Axes or list of Axes
single instance or list of matplotlib.axes.Axes objects. This are the axes in the
figures in the animation. More info at
https://matplotlib.org/stable/api/axes_api.html?highlight=axes#module-matplotlib.axes
init_temp : float
the initial temperature of the lattice as a whole.
temp : float
the current temperature of the lattice, in energy units.
A new value can be assigned anytime.
final_temp : float
the final temperature of the system.
cooling_rate : float
the rate with which the temperature will find its way to the final_temp.
(1 / cooling_rate) is the amount of time (in seconds) it takes to achieve about
63% of the way there.
field : float
the current value of the external magnetic field, oriented
perpendicularlly to the lattice. A positive value represents
a up oriented field. A new value can be assigned anytime.
energy : float
the total energy of the lattice in its current generation.
mag_mom : float
the total magnetic moment of the lattice in its current generation.
mean_energy_hist : list[float]
a list with the values of the mean energy for each past generation.
New values are appended by a call to the update function
magnet_hist : list[float]
a list with the values of the magnetization per spin
for each past generation. New values are appended by a call to
the update function
specific_heat_hist : list[float]
a list with the values of the specific heat per spin
for each past generation. New values are appended by a call to
the update function
susceptibility_hist : list[float]
a list with the values of the magnetic susceptibility
for each past generation. New values are appended by a call to
the update function
"""
def __init__(
self,
shape=(128, 128),
temp=5,
final_temp=1,
cooling_rate=0.5,
j=(1, 1),
field=0,
init_state="random",
time_series=False,
interval=100,
frames=100,
) -> None:
super().__init__(
shape=shape,
temp=temp,
j=j,
field=field,
init_state=init_state,
time_series=time_series,
interval=interval,
frames=frames,
)
self._init_temp = abs(float(self.temp))
self._final_temp = abs(float(final_temp))
self._cooling_rate = abs(float(cooling_rate))
def __repr__(self) -> str:
return (
f"CoolingAnimatedIsing(shape={self.lattice.shape.__str__()}, "
+ f"temp={self.lattice.temp}, "
+ f"final_temp={self.final_temp}, "
+ f"cooling_rate={self.cooling_rate}, "
+ f"j={self.lattice.j.__str__()}, "
+ f"field={self.lattice.field}, "
+ f"time_series={self.time_series}, "
+ f"interval={self.interval}, "
+ f"frames={self.frames})"
)
@property
def init_temp(self):
return self._init_temp
@property
def final_temp(self):
return self._final_temp
@property
def cooling_rate(self):
return self._cooling_rate
def update(self):
"""
Updates the system to the next generation, appending new values to
the history list of each phisical quantity. This function is automatically
called by the animation attribute to render the next frame.
"""
super().update()
self.temp = self.final_temp + (self.init_temp - self.final_temp) * exp(
-self.cooling_rate * self.time
)
class DynamicAnimatedIsing(Ising):
"""
Animation of the Ising Model with both temperature and external magnetic
field varying as functions of time
Args
------------------
shape : 2-tuple of ints; Default is (128, 128)
the shape of the lattice of spins.
temp : callable; Default is lambda t: 2.0
a real valued one variable function that describes the temperature in
the interval [0, interval * frames / 1000]
j : float or 2-tuple of floats; Default is 1.0
the coefficient of interaction between neighboring spins in the lattice.
when a tuple is suplied, the first value is the coefficient for row neighbors
and the second value is the coefficient for column neighbors.
field : callable; Default is lambda t: math.sin(t)
a real valued one variable function that describes the external
magnetic field in the interval [0, interval * frames / 1000]
init_state : {"random", "down", "up"}; Default is "random"
the initial configuration of the spins in the lattice.
time_series : bool. Default is False
wheater or not to include the time series of the macroscopic
physical quantities in the animation
interval : int. Default is 100
the interval between each frame in the animation, in milliseconds
frames : int. Default is 60
the number of frames to include in the animation
Attributes
------------------
gen : int
the current generation of the system. Starts at 0 and is
incremented by a call to update method
init_state : {"random", "down", "up"}; Default is "random"
the initial configuration of the spins in the lattice.
spins : int
the number of the spins in the lattice
lattice : Lattice
an instance of a Lattice object that describes the
current state of the system
animation : FuncAnimation
a matplotlib.animation.FuncAnimation object. The animation is saved
with a call to animation.save("outfile.gif"). More info at
https://matplotlib.org/stable/api/_as_gen/matplotlib.animation.FuncAnimation.html
fig : Figure
a matplotlib.figure.Figure object in which the animation takes place. More info at
https://matplotlib.org/stable/api/figure_api.html?highlight=figure#matplotlib.figure.Figure
ax : Axes or list of Axes
single instance or list of matplotlib.axes.Axes objects. This are the axes in the
figures in the animation. More info at
https://matplotlib.org/stable/api/axes_api.html?highlight=axes#module-matplotlib.axes
temp : float
the current temperature of the lattice, in energy units.
A new value can be assigned anytime.
field : float
the current value of the external magnetic field, oriented
perpendicularlly to the lattice. A positive value represents
a up oriented field. A new value can be assigned anytime.
temp_func : callable
the function passed as temp to the constructor
field_func : callable
the function passed as field to the constructor
energy : float
the total energy of the lattice in its current generation.
mag_mom : float
the total magnetic moment of the lattice in its current generation.
mean_energy_hist : list[float]
a list with the values of the mean energy for each past generation.
New values are appended by a call to the update function
magnet_hist : list[float]
a list with the values of the magnetization per spin
for each past generation. New values are appended by a call to
the update function
specific_heat_hist : list[float]
a list with the values of the specific heat per spin
for each past generation. New values are appended by a call to
the update function
susceptibility_hist : list[float]
a list with the values of the magnetic susceptibility
for each past generation. New values are appended by a call to
the update function
"""
def __init__(
self,
shape=(128, 128),
temp: callable = lambda t: 2.0,
j=(1, 1),
field: callable = lambda t: sin(t),
init_state="random",
time_series=False,
interval=100,
frames=60,
) -> None:
super().__init__(
shape=shape,
temp=temp(0),
j=j,
field=field(0),
init_state=init_state,
)
self.temp_func = temp
self.field_func = field
self.time_series = bool(time_series)
if self.time_series:
self.fig, self.ax = plt.subplots(4, 2)
self.fig.set_size_inches(10.8, 9.6)
# Merging axis [0, 0] and [1, 0]
gridspec = self.ax[0, 0].get_gridspec()
for ax in self.ax[0:2, 0]:
ax.remove()
self.fig.add_subplot(gridspec[0:2, 0])
self.ax = self.fig.get_axes() # ax[0, 0] is now ax[4]
self.ax.insert(0, self.ax.pop()) # ax[4] is now ax[0]
self.__update_animation = self.__update_ani_time_series
self.__init_animation = self.__init_ani_time_series
else:
self.fig, self.ax = plt.subplots(2, 2)
self.fig.set_size_inches(10.8, 4.8)
# Merging axes [0, 0] and [1, 0]
gridspec = self.ax[0, 0].get_gridspec()
for ax in self.ax[:, 0]:
ax.remove()
self.fig.add_subplot(gridspec[:, 0])
self.ax = self.fig.get_axes() # ax[0, 0] is now ax[2]
self.ax.insert(0, self.ax.pop()) # ax[2] is now ax[0]
self.__update_animation = self.__update_ani_no_time_series
self.__init_animation = self.__init_ani_no_time_series
self.fig.suptitle(self.__str__())
self.interval = interval
self.frames = frames
self.time_hist = [self.time]
self.temp_hist = [self.temp]
self.field_hist = [self.field]
self.animation = FuncAnimation(
self.fig,
func=self.__update_animation,
init_func=self.__init_animation,
interval=self.interval,
save_count=self.frames,
)
self.axes_labels = {
"time": r"$t$",
"energy": r"$\langle E \rangle$",
"magnet": r"$\langle \mu \rangle / n$",
"specific_heat": r"$C / n$",
"susceptibility": r"$\chi$",
"temp": r"$T$",
"field": r"$H_z$",
}
def __repr__(self) -> str:
return (
f"DynamicAnimatedIsing(shape={self.lattice.shape.__str__()}, "
+ f"temp={self.temp_func.__name__}, "
+ f"j={self.lattice.j.__str__()}, "
+ f"field={self.field_func.__name__}, "
+ f"time_series={self.time_series}, "
+ f"interval={self.interval}, "
+ f"frames={self.frames})"
)
@property
def time(self):
return self.gen * self.interval / 1000
def update(self):
"""
Updates the system to the next generation, appending new values to
the history list of each phisical quantity. This function is automatically
called by the animation attribute to render the next frame.
"""
self.temp = self.temp_func(self.time)
self.field = self.field_func(self.time)
super().update()
self.time_hist.append(self.time)
self.temp_hist.append(self.temp)
self.field_hist.append(self.field)
def __set_axes_time_series(self):
for ax in self.ax[1:]:
ax.yaxis.set_major_formatter(StrMethodFormatter("{x:.1e}"))
ax.set(
xlim=(0, self.frames * self.interval / 1000),
xlabel=self.axes_labels["time"],
)
ax.grid(linestyle=":")
self.ax[0].set(ylabel="i", xlabel="j")
self.ax[1].set(ylabel=self.axes_labels["energy"])
self.ax[2].set(ylabel=self.axes_labels["magnet"])
self.ax[3].set(ylabel=self.axes_labels["specific_heat"])
self.ax[4].set(ylabel=self.axes_labels["susceptibility"])
self.ax[5].set(ylabel=self.axes_labels["temp"])
self.ax[6].set(ylabel=self.axes_labels["field"])
def __init_ani_time_series(self):
self.__set_axes_time_series()
self.ax[0].imshow(self.lattice.state, norm=Normalize(vmin=-1.0, vmax=1.0))
def __update_ani_time_series(self, frame):
for ax in self.ax:
ax.clear()
self.update()
self.__set_axes_time_series()
self.fig.suptitle(self.__str__())
self.ax[0].imshow(self.lattice.state, norm=Normalize(vmin=-1.0, vmax=1.0))
self.ax[1].plot(self.time_hist, self.mean_energy_hist, color="purple")
self.ax[2].plot(self.time_hist, self.magnet_hist, color="purple")
self.ax[3].plot(self.time_hist, self.specific_heat_hist, color="purple")
self.ax[4].plot(self.time_hist, self.susceptibility_hist, color="purple")
self.ax[5].plot(self.time_hist, self.temp_hist, color="purple")
self.ax[6].plot(self.time_hist, self.field_hist, color="purple")
def __set_axes_no_time_series(self):
for ax in self.ax[1:]:
ax.yaxis.set_major_formatter(StrMethodFormatter("{x:.1e}"))
ax.set(
xlim=(0, self.frames * self.interval / 1000),
xlabel=self.axes_labels["time"],
)
ax.grid(linestyle=":")
self.ax[0].set(ylabel="i", xlabel="j")
self.ax[1].set(ylabel=self.axes_labels["temp"])
self.ax[2].set(ylabel=self.axes_labels["field"])
def __init_ani_no_time_series(self):
self.__set_axes_no_time_series()
self.ax[0].imshow(self.lattice.state, norm=Normalize(vmin=-1.0, vmax=1.0))
def __update_ani_no_time_series(self, frame):
for ax in self.ax:
ax.clear()
self.update()
self.__set_axes_no_time_series()
self.fig.suptitle(self.__str__())
self.ax[0].imshow(self.lattice.state, norm=Normalize(vmin=-1.0, vmax=1.0))
self.ax[1].plot(self.time_hist, self.temp_hist, color="purple")
self.ax[2].plot(self.time_hist, self.field_hist, color="purple")Classes
class AnimatedIsing (shape=(128, 128), temp=2, j=(1, 1), field=0, init_state='random', time_series=False, interval=100, frames=60)-
Animation of the Ising Model at constant temperature and constant external magnetic field
Args
shape:2-tupleofints. Default is (128, 128)- the shape of the lattice of spins.
temp:float. Default is 2.0- the initial temperature of the lattice as a whole.
j:floator2-tupleoffloats. Default is 1.0- the coefficient of interaction between neighboring spins in the lattice. when a tuple is suplied, the first value is the coefficient for row neighbors and the second value is the coefficient for column neighbors.
field:float. Default is 0.0- the initial value for the external magnetic field.
init_state:{"random", "down", "up"}. Default is "random"- the initial configuration of the spins in the lattice.
time_series:bool. Default is False- wheater or not to include the time series of the macroscopic physical quantities in the animation
interval:int. Default is 100- the interval between each frame in the animation, in milliseconds
frames:int. Default is 60- the number of frames to include in the animation
Attributes
gen:int- the current generation of the system. Starts at 0 and is incremented by a call to update method
interval:int- the interval between each frame in the animation, in milliseconds
frames : int. the number of frames to include in the animation
time:float- elapsed time, considering one update per frame
init_state:{"random", "down", "up"}; Default is "random"- the initial configuration of the spins in the lattice.
spins:int- the number of the spins in the lattice
lattice:Lattice- an instance of a Lattice object that describes the current state of the system
animation:FuncAnimation- a matplotlib.animation.FuncAnimation object. The animation is saved with a call to animation.save("outfile.gif"). More info at https://matplotlib.org/stable/api/_as_gen/matplotlib.animation.FuncAnimation.html
fig:Figure- a matplotlib.figure.Figure object in which the animation takes place. More info at https://matplotlib.org/stable/api/figure_api.html?highlight=figure#matplotlib.figure.Figure
ax:AxesorlistofAxes- single instance or list of matplotlib.axes.Axes objects. This are the axes in the figures in the animation. More info at https://matplotlib.org/stable/api/axes_api.html?highlight=axes#module-matplotlib.axes
temp:float- the current temperature of the lattice, in energy units. A new value can be assigned anytime.
field:float- the current value of the external magnetic field, oriented perpendicularlly to the lattice. A positive value represents a up oriented field. A new value can be assigned anytime.
energy:float- the total energy of the lattice in its current generation.
mag_mom:float- the total magnetic moment of the lattice in its current generation.
time_hist:list[float]- a list with the values of time for each past generation. New values are appended by a call to the update function
mean_energy_hist:list[float]- a list with the values of the mean energy for each past generation. New values are appended by a call to the update function
magnet_hist:list[float]- a list with the values of the magnetization per spin for each past generation. New values are appended by a call to the update function
specific_heat_hist:list[float]- a list with the values of the specific heat per spin for each past generation. New values are appended by a call to the update function
susceptibility_hist:list[float]- a list with the values of the magnetic susceptibility for each past generation. New values are appended by a call to the update function
Expand source code
class AnimatedIsing(Ising): """ Animation of the Ising Model at constant temperature and constant external magnetic field Args ------------------ shape : 2-tuple of ints. Default is (128, 128) the shape of the lattice of spins. temp : float. Default is 2.0 the initial temperature of the lattice as a whole. j : float or 2-tuple of floats. Default is 1.0 the coefficient of interaction between neighboring spins in the lattice. when a tuple is suplied, the first value is the coefficient for row neighbors and the second value is the coefficient for column neighbors. field : float. Default is 0.0 the initial value for the external magnetic field. init_state : {"random", "down", "up"}. Default is "random" the initial configuration of the spins in the lattice. time_series : bool. Default is False wheater or not to include the time series of the macroscopic physical quantities in the animation interval : int. Default is 100 the interval between each frame in the animation, in milliseconds frames : int. Default is 60 the number of frames to include in the animation Attributes ------------------ gen : int the current generation of the system. Starts at 0 and is incremented by a call to update method interval : int the interval between each frame in the animation, in milliseconds frames : int. the number of frames to include in the animation time : float elapsed time, considering one update per frame init_state : {"random", "down", "up"}; Default is "random" the initial configuration of the spins in the lattice. spins : int the number of the spins in the lattice lattice : Lattice an instance of a Lattice object that describes the current state of the system animation : FuncAnimation a matplotlib.animation.FuncAnimation object. The animation is saved with a call to animation.save("outfile.gif"). More info at https://matplotlib.org/stable/api/_as_gen/matplotlib.animation.FuncAnimation.html fig : Figure a matplotlib.figure.Figure object in which the animation takes place. More info at https://matplotlib.org/stable/api/figure_api.html?highlight=figure#matplotlib.figure.Figure ax : Axes or list of Axes single instance or list of matplotlib.axes.Axes objects. This are the axes in the figures in the animation. More info at https://matplotlib.org/stable/api/axes_api.html?highlight=axes#module-matplotlib.axes temp : float the current temperature of the lattice, in energy units. A new value can be assigned anytime. field : float the current value of the external magnetic field, oriented perpendicularlly to the lattice. A positive value represents a up oriented field. A new value can be assigned anytime. energy : float the total energy of the lattice in its current generation. mag_mom : float the total magnetic moment of the lattice in its current generation. time_hist : list[float] a list with the values of time for each past generation. New values are appended by a call to the update function mean_energy_hist : list[float] a list with the values of the mean energy for each past generation. New values are appended by a call to the update function magnet_hist : list[float] a list with the values of the magnetization per spin for each past generation. New values are appended by a call to the update function specific_heat_hist : list[float] a list with the values of the specific heat per spin for each past generation. New values are appended by a call to the update function susceptibility_hist : list[float] a list with the values of the magnetic susceptibility for each past generation. New values are appended by a call to the update function """ def __init__( self, shape=(128, 128), temp=2, j=(1, 1), field=0, init_state="random", time_series=False, interval=100, frames=60, ) -> None: super().__init__( shape=shape, temp=temp, j=j, field=field, init_state=init_state, ) self.time_series = bool(time_series) if self.time_series: self.fig, self.ax = plt.subplots(3, 2) self.fig.set_size_inches(10.8, 7.2) # Merging axis [0, 0] and [1, 0] gridspec = self.ax[0, 0].get_gridspec() for ax in self.ax[0:2, 0]: ax.remove() self.fig.add_subplot(gridspec[0:2, 0]) self.ax = self.fig.get_axes() # ax[0, 0] is now ax[4] self.ax.insert(0, self.ax.pop()) # ax[4] is now ax[0] self.__update_animation = self.__update_ani_time_series self.__init_animation = self.__init_ani_time_series else: self.fig, self.ax = plt.subplots() self.fig.set_size_inches(7.2, 4.8) self.__update_animation = self.__update_ani_no_time_series self.__init_animation = self.__init_ani_no_time_series self.fig.suptitle(self.__str__()) self.interval = interval self.frames = frames self.time_hist = [self.time] self.animation = FuncAnimation( self.fig, func=self.__update_animation, init_func=self.__init_animation, interval=self.interval, save_count=self.frames, ) self.axes_labels = { "time": r"$t$", "energy": r"$\langle E \rangle$", "magnet": r"$\langle \mu \rangle / n$", "specific_heat": r"$C / n$", "susceptibility": r"$\chi$", } def __repr__(self) -> str: return ( f"AnimatedIsing(shape={self.lattice.shape.__str__()}, " + f"temp={self.lattice.temp}, " + f"j={self.lattice.j.__str__()}, " + f"field={self.lattice.field}, " + f"time_series={self.time_series}, " + f"interval={self.interval}, " + f"frames={self.frames})" ) @property def time(self): return self.gen * self.interval / 1000 def update(self): """ Updates the system to the next generation, appending new values to the history list of each phisical quantity. This function is automatically called by the animation attribute to render the next frame. """ super().update() self.time_hist.append(self.time) def __set_axes(self): for ax in self.ax[1:]: ax.yaxis.set_major_formatter(StrMethodFormatter("{x:.1e}")) ax.set( xlim=(0, self.frames * self.interval / 1000), xlabel=self.axes_labels["time"], ) ax.grid(linestyle=":") self.ax[0].set(ylabel="i", xlabel="j") self.ax[1].set(ylabel=self.axes_labels["energy"]) self.ax[2].set(ylabel=self.axes_labels["magnet"]) self.ax[3].set(ylabel=self.axes_labels["specific_heat"]) self.ax[4].set(ylabel=self.axes_labels["susceptibility"]) def __init_ani_time_series(self): self.__set_axes() self.ax[0].imshow(self.lattice.state, norm=Normalize(vmin=-1.0, vmax=1.0)) def __update_ani_time_series(self, frame): for ax in self.ax: ax.clear() self.update() self.__set_axes() self.fig.suptitle(self.__str__()) self.ax[0].imshow(self.lattice.state, norm=Normalize(vmin=-1.0, vmax=1.0)) self.ax[1].plot(self.time_hist, self.mean_energy_hist, color="purple") self.ax[2].plot(self.time_hist, self.magnet_hist, color="purple") self.ax[3].plot(self.time_hist, self.specific_heat_hist, color="purple") self.ax[4].plot(self.time_hist, self.susceptibility_hist, color="purple") def __init_ani_no_time_series(self): self.ax.set(ylabel="i", xlabel="j") self.ax.imshow(self.lattice.state, norm=Normalize(vmin=-1.0, vmax=1.0)) def __update_ani_no_time_series(self, frame): self.ax.clear() self.update() self.ax.set(ylabel="i", xlabel="j") self.fig.suptitle(self.__str__()) self.ax.imshow(self.lattice.state, norm=Normalize(vmin=-1.0, vmax=1.0))Ancestors
Subclasses
Instance variables
var time-
Expand source code
@property def time(self): return self.gen * self.interval / 1000
Methods
def update(self)-
Updates the system to the next generation, appending new values to the history list of each phisical quantity. This function is automatically called by the animation attribute to render the next frame.
Expand source code
def update(self): """ Updates the system to the next generation, appending new values to the history list of each phisical quantity. This function is automatically called by the animation attribute to render the next frame. """ super().update() self.time_hist.append(self.time)
class CoolingAnimatedIsing (shape=(128, 128), temp=5, final_temp=1, cooling_rate=0.5, j=(1, 1), field=0, init_state='random', time_series=False, interval=100, frames=100)-
Animation of the Ising Model at constant external magnetic field, but with its temperature growing (or decaing) exponentially, given initial and target values.
Args
shape:2-tupleofints- the shape of the lattice of spins. Default is (128, 128).
temp:float. Default is 5.0- the initial temperature of the lattice as a whole.
final_temp:float. Default is 1.0- the final temperature of the system.
cooling_rate:float. Default is 0.5- the rate with which the temperature will find its way to the final_temp. (1 / cooling_rate) is the amount of time (in seconds) it takes to achieve about 63% of the way there.
j:floator2-tupleoffloats. Default is (1.0, 1.0)- the coefficient of interaction between neighboring spins in the lattice. when a tuple is suplied, the first value is the coefficient for row neighbors and the second value is the coefficient for column neighbors.
field:float. Default is 0.0- the initial value for the external magnetic field.
init_state:{"random", "down", "up"}. Default is "random"- the initial configuration of the spins in the lattice.
time_series:bool. Default is False- wheater or not to include the time series of the macroscopic physical quantities in the animation
interval:int. Default is 100- the interval between each frame in the animation, in milliseconds
frames:int. Default is 60- the number of frames to include in the animation
Attributes
gen:int- the current generation of the system. Starts at 0 and is incremented by a call to update method
init_state:{"random", "down", "up"}; Default is "random"- the initial configuration of the spins in the lattice.
spins:int- the number of the spins in the lattice
lattice:Lattice- an instance of a Lattice object that describes the current state of the system
animation:FuncAnimation- a matplotlib.animation.FuncAnimation object. The animation is saved with a call to animation.save("outfile.gif"). More info at https://matplotlib.org/stable/api/_as_gen/matplotlib.animation.FuncAnimation.html
fig:Figure- a matplotlib.figure.Figure object in which the animation takes place. More info at https://matplotlib.org/stable/api/figure_api.html?highlight=figure#matplotlib.figure.Figure
ax:AxesorlistofAxes- single instance or list of matplotlib.axes.Axes objects. This are the axes in the figures in the animation. More info at https://matplotlib.org/stable/api/axes_api.html?highlight=axes#module-matplotlib.axes
init_temp:float- the initial temperature of the lattice as a whole.
temp:float- the current temperature of the lattice, in energy units. A new value can be assigned anytime.
final_temp:float- the final temperature of the system.
cooling_rate:float- the rate with which the temperature will find its way to the final_temp. (1 / cooling_rate) is the amount of time (in seconds) it takes to achieve about 63% of the way there.
field:float- the current value of the external magnetic field, oriented perpendicularlly to the lattice. A positive value represents a up oriented field. A new value can be assigned anytime.
energy:float- the total energy of the lattice in its current generation.
mag_mom:float- the total magnetic moment of the lattice in its current generation.
mean_energy_hist:list[float]- a list with the values of the mean energy for each past generation. New values are appended by a call to the update function
magnet_hist:list[float]- a list with the values of the magnetization per spin for each past generation. New values are appended by a call to the update function
specific_heat_hist:list[float]- a list with the values of the specific heat per spin for each past generation. New values are appended by a call to the update function
susceptibility_hist:list[float]- a list with the values of the magnetic susceptibility for each past generation. New values are appended by a call to the update function
Expand source code
class CoolingAnimatedIsing(AnimatedIsing): """ Animation of the Ising Model at constant external magnetic field, but with its temperature growing (or decaing) exponentially, given initial and target values. Args ------------------ shape : 2-tuple of ints the shape of the lattice of spins. Default is (128, 128). temp : float. Default is 5.0 the initial temperature of the lattice as a whole. final_temp : float. Default is 1.0 the final temperature of the system. cooling_rate : float. Default is 0.5 the rate with which the temperature will find its way to the final_temp. (1 / cooling_rate) is the amount of time (in seconds) it takes to achieve about 63% of the way there. j : float or 2-tuple of floats. Default is (1.0, 1.0) the coefficient of interaction between neighboring spins in the lattice. when a tuple is suplied, the first value is the coefficient for row neighbors and the second value is the coefficient for column neighbors. field : float. Default is 0.0 the initial value for the external magnetic field. init_state : {"random", "down", "up"}. Default is "random" the initial configuration of the spins in the lattice. time_series : bool. Default is False wheater or not to include the time series of the macroscopic physical quantities in the animation interval : int. Default is 100 the interval between each frame in the animation, in milliseconds frames : int. Default is 60 the number of frames to include in the animation Attributes ------------------ gen : int the current generation of the system. Starts at 0 and is incremented by a call to update method init_state : {"random", "down", "up"}; Default is "random" the initial configuration of the spins in the lattice. spins : int the number of the spins in the lattice lattice : Lattice an instance of a Lattice object that describes the current state of the system animation : FuncAnimation a matplotlib.animation.FuncAnimation object. The animation is saved with a call to animation.save("outfile.gif"). More info at https://matplotlib.org/stable/api/_as_gen/matplotlib.animation.FuncAnimation.html fig : Figure a matplotlib.figure.Figure object in which the animation takes place. More info at https://matplotlib.org/stable/api/figure_api.html?highlight=figure#matplotlib.figure.Figure ax : Axes or list of Axes single instance or list of matplotlib.axes.Axes objects. This are the axes in the figures in the animation. More info at https://matplotlib.org/stable/api/axes_api.html?highlight=axes#module-matplotlib.axes init_temp : float the initial temperature of the lattice as a whole. temp : float the current temperature of the lattice, in energy units. A new value can be assigned anytime. final_temp : float the final temperature of the system. cooling_rate : float the rate with which the temperature will find its way to the final_temp. (1 / cooling_rate) is the amount of time (in seconds) it takes to achieve about 63% of the way there. field : float the current value of the external magnetic field, oriented perpendicularlly to the lattice. A positive value represents a up oriented field. A new value can be assigned anytime. energy : float the total energy of the lattice in its current generation. mag_mom : float the total magnetic moment of the lattice in its current generation. mean_energy_hist : list[float] a list with the values of the mean energy for each past generation. New values are appended by a call to the update function magnet_hist : list[float] a list with the values of the magnetization per spin for each past generation. New values are appended by a call to the update function specific_heat_hist : list[float] a list with the values of the specific heat per spin for each past generation. New values are appended by a call to the update function susceptibility_hist : list[float] a list with the values of the magnetic susceptibility for each past generation. New values are appended by a call to the update function """ def __init__( self, shape=(128, 128), temp=5, final_temp=1, cooling_rate=0.5, j=(1, 1), field=0, init_state="random", time_series=False, interval=100, frames=100, ) -> None: super().__init__( shape=shape, temp=temp, j=j, field=field, init_state=init_state, time_series=time_series, interval=interval, frames=frames, ) self._init_temp = abs(float(self.temp)) self._final_temp = abs(float(final_temp)) self._cooling_rate = abs(float(cooling_rate)) def __repr__(self) -> str: return ( f"CoolingAnimatedIsing(shape={self.lattice.shape.__str__()}, " + f"temp={self.lattice.temp}, " + f"final_temp={self.final_temp}, " + f"cooling_rate={self.cooling_rate}, " + f"j={self.lattice.j.__str__()}, " + f"field={self.lattice.field}, " + f"time_series={self.time_series}, " + f"interval={self.interval}, " + f"frames={self.frames})" ) @property def init_temp(self): return self._init_temp @property def final_temp(self): return self._final_temp @property def cooling_rate(self): return self._cooling_rate def update(self): """ Updates the system to the next generation, appending new values to the history list of each phisical quantity. This function is automatically called by the animation attribute to render the next frame. """ super().update() self.temp = self.final_temp + (self.init_temp - self.final_temp) * exp( -self.cooling_rate * self.time )Ancestors
Instance variables
var cooling_rate-
Expand source code
@property def cooling_rate(self): return self._cooling_rate var final_temp-
Expand source code
@property def final_temp(self): return self._final_temp var init_temp-
Expand source code
@property def init_temp(self): return self._init_temp
Inherited members
class DynamicAnimatedIsing (shape=(128, 128), temp:-
Animation of the Ising Model with both temperature and external magnetic field varying as functions of time
Args
shape:2-tupleofints; Default is (128, 128)- the shape of the lattice of spins.
temp:callable; Default is lambda t: 2.0- a real valued one variable function that describes the temperature in the interval [0, interval * frames / 1000]
j:floator2-tupleoffloats; Default is 1.0- the coefficient of interaction between neighboring spins in the lattice. when a tuple is suplied, the first value is the coefficient for row neighbors and the second value is the coefficient for column neighbors.
field:callable; Default is lambda t: math.sin(t)- a real valued one variable function that describes the external magnetic field in the interval [0, interval * frames / 1000]
init_state:{"random", "down", "up"}; Default is "random"- the initial configuration of the spins in the lattice.
time_series:bool. Default is False- wheater or not to include the time series of the macroscopic physical quantities in the animation
interval:int. Default is 100- the interval between each frame in the animation, in milliseconds
frames:int. Default is 60- the number of frames to include in the animation
Attributes
gen:int- the current generation of the system. Starts at 0 and is incremented by a call to update method
init_state:{"random", "down", "up"}; Default is "random"- the initial configuration of the spins in the lattice.
spins:int- the number of the spins in the lattice
lattice:Lattice- an instance of a Lattice object that describes the current state of the system
animation:FuncAnimation- a matplotlib.animation.FuncAnimation object. The animation is saved with a call to animation.save("outfile.gif"). More info at https://matplotlib.org/stable/api/_as_gen/matplotlib.animation.FuncAnimation.html
fig:Figure- a matplotlib.figure.Figure object in which the animation takes place. More info at https://matplotlib.org/stable/api/figure_api.html?highlight=figure#matplotlib.figure.Figure
ax:AxesorlistofAxes- single instance or list of matplotlib.axes.Axes objects. This are the axes in the figures in the animation. More info at https://matplotlib.org/stable/api/axes_api.html?highlight=axes#module-matplotlib.axes
temp:float- the current temperature of the lattice, in energy units. A new value can be assigned anytime.
field:float- the current value of the external magnetic field, oriented perpendicularlly to the lattice. A positive value represents a up oriented field. A new value can be assigned anytime.
temp_func:callable- the function passed as temp to the constructor
field_func:callable- the function passed as field to the constructor
energy:float- the total energy of the lattice in its current generation.
mag_mom:float- the total magnetic moment of the lattice in its current generation.
mean_energy_hist:list[float]- a list with the values of the mean energy for each past generation. New values are appended by a call to the update function
magnet_hist:list[float]- a list with the values of the magnetization per spin for each past generation. New values are appended by a call to the update function
specific_heat_hist:list[float]- a list with the values of the specific heat per spin for each past generation. New values are appended by a call to the update function
susceptibility_hist:list[float]- a list with the values of the magnetic susceptibility for each past generation. New values are appended by a call to the update function
Expand source code
class DynamicAnimatedIsing(Ising): """ Animation of the Ising Model with both temperature and external magnetic field varying as functions of time Args ------------------ shape : 2-tuple of ints; Default is (128, 128) the shape of the lattice of spins. temp : callable; Default is lambda t: 2.0 a real valued one variable function that describes the temperature in the interval [0, interval * frames / 1000] j : float or 2-tuple of floats; Default is 1.0 the coefficient of interaction between neighboring spins in the lattice. when a tuple is suplied, the first value is the coefficient for row neighbors and the second value is the coefficient for column neighbors. field : callable; Default is lambda t: math.sin(t) a real valued one variable function that describes the external magnetic field in the interval [0, interval * frames / 1000] init_state : {"random", "down", "up"}; Default is "random" the initial configuration of the spins in the lattice. time_series : bool. Default is False wheater or not to include the time series of the macroscopic physical quantities in the animation interval : int. Default is 100 the interval between each frame in the animation, in milliseconds frames : int. Default is 60 the number of frames to include in the animation Attributes ------------------ gen : int the current generation of the system. Starts at 0 and is incremented by a call to update method init_state : {"random", "down", "up"}; Default is "random" the initial configuration of the spins in the lattice. spins : int the number of the spins in the lattice lattice : Lattice an instance of a Lattice object that describes the current state of the system animation : FuncAnimation a matplotlib.animation.FuncAnimation object. The animation is saved with a call to animation.save("outfile.gif"). More info at https://matplotlib.org/stable/api/_as_gen/matplotlib.animation.FuncAnimation.html fig : Figure a matplotlib.figure.Figure object in which the animation takes place. More info at https://matplotlib.org/stable/api/figure_api.html?highlight=figure#matplotlib.figure.Figure ax : Axes or list of Axes single instance or list of matplotlib.axes.Axes objects. This are the axes in the figures in the animation. More info at https://matplotlib.org/stable/api/axes_api.html?highlight=axes#module-matplotlib.axes temp : float the current temperature of the lattice, in energy units. A new value can be assigned anytime. field : float the current value of the external magnetic field, oriented perpendicularlly to the lattice. A positive value represents a up oriented field. A new value can be assigned anytime. temp_func : callable the function passed as temp to the constructor field_func : callable the function passed as field to the constructor energy : float the total energy of the lattice in its current generation. mag_mom : float the total magnetic moment of the lattice in its current generation. mean_energy_hist : list[float] a list with the values of the mean energy for each past generation. New values are appended by a call to the update function magnet_hist : list[float] a list with the values of the magnetization per spin for each past generation. New values are appended by a call to the update function specific_heat_hist : list[float] a list with the values of the specific heat per spin for each past generation. New values are appended by a call to the update function susceptibility_hist : list[float] a list with the values of the magnetic susceptibility for each past generation. New values are appended by a call to the update function """ def __init__( self, shape=(128, 128), temp: callable = lambda t: 2.0, j=(1, 1), field: callable = lambda t: sin(t), init_state="random", time_series=False, interval=100, frames=60, ) -> None: super().__init__( shape=shape, temp=temp(0), j=j, field=field(0), init_state=init_state, ) self.temp_func = temp self.field_func = field self.time_series = bool(time_series) if self.time_series: self.fig, self.ax = plt.subplots(4, 2) self.fig.set_size_inches(10.8, 9.6) # Merging axis [0, 0] and [1, 0] gridspec = self.ax[0, 0].get_gridspec() for ax in self.ax[0:2, 0]: ax.remove() self.fig.add_subplot(gridspec[0:2, 0]) self.ax = self.fig.get_axes() # ax[0, 0] is now ax[4] self.ax.insert(0, self.ax.pop()) # ax[4] is now ax[0] self.__update_animation = self.__update_ani_time_series self.__init_animation = self.__init_ani_time_series else: self.fig, self.ax = plt.subplots(2, 2) self.fig.set_size_inches(10.8, 4.8) # Merging axes [0, 0] and [1, 0] gridspec = self.ax[0, 0].get_gridspec() for ax in self.ax[:, 0]: ax.remove() self.fig.add_subplot(gridspec[:, 0]) self.ax = self.fig.get_axes() # ax[0, 0] is now ax[2] self.ax.insert(0, self.ax.pop()) # ax[2] is now ax[0] self.__update_animation = self.__update_ani_no_time_series self.__init_animation = self.__init_ani_no_time_series self.fig.suptitle(self.__str__()) self.interval = interval self.frames = frames self.time_hist = [self.time] self.temp_hist = [self.temp] self.field_hist = [self.field] self.animation = FuncAnimation( self.fig, func=self.__update_animation, init_func=self.__init_animation, interval=self.interval, save_count=self.frames, ) self.axes_labels = { "time": r"$t$", "energy": r"$\langle E \rangle$", "magnet": r"$\langle \mu \rangle / n$", "specific_heat": r"$C / n$", "susceptibility": r"$\chi$", "temp": r"$T$", "field": r"$H_z$", } def __repr__(self) -> str: return ( f"DynamicAnimatedIsing(shape={self.lattice.shape.__str__()}, " + f"temp={self.temp_func.__name__}, " + f"j={self.lattice.j.__str__()}, " + f"field={self.field_func.__name__}, " + f"time_series={self.time_series}, " + f"interval={self.interval}, " + f"frames={self.frames})" ) @property def time(self): return self.gen * self.interval / 1000 def update(self): """ Updates the system to the next generation, appending new values to the history list of each phisical quantity. This function is automatically called by the animation attribute to render the next frame. """ self.temp = self.temp_func(self.time) self.field = self.field_func(self.time) super().update() self.time_hist.append(self.time) self.temp_hist.append(self.temp) self.field_hist.append(self.field) def __set_axes_time_series(self): for ax in self.ax[1:]: ax.yaxis.set_major_formatter(StrMethodFormatter("{x:.1e}")) ax.set( xlim=(0, self.frames * self.interval / 1000), xlabel=self.axes_labels["time"], ) ax.grid(linestyle=":") self.ax[0].set(ylabel="i", xlabel="j") self.ax[1].set(ylabel=self.axes_labels["energy"]) self.ax[2].set(ylabel=self.axes_labels["magnet"]) self.ax[3].set(ylabel=self.axes_labels["specific_heat"]) self.ax[4].set(ylabel=self.axes_labels["susceptibility"]) self.ax[5].set(ylabel=self.axes_labels["temp"]) self.ax[6].set(ylabel=self.axes_labels["field"]) def __init_ani_time_series(self): self.__set_axes_time_series() self.ax[0].imshow(self.lattice.state, norm=Normalize(vmin=-1.0, vmax=1.0)) def __update_ani_time_series(self, frame): for ax in self.ax: ax.clear() self.update() self.__set_axes_time_series() self.fig.suptitle(self.__str__()) self.ax[0].imshow(self.lattice.state, norm=Normalize(vmin=-1.0, vmax=1.0)) self.ax[1].plot(self.time_hist, self.mean_energy_hist, color="purple") self.ax[2].plot(self.time_hist, self.magnet_hist, color="purple") self.ax[3].plot(self.time_hist, self.specific_heat_hist, color="purple") self.ax[4].plot(self.time_hist, self.susceptibility_hist, color="purple") self.ax[5].plot(self.time_hist, self.temp_hist, color="purple") self.ax[6].plot(self.time_hist, self.field_hist, color="purple") def __set_axes_no_time_series(self): for ax in self.ax[1:]: ax.yaxis.set_major_formatter(StrMethodFormatter("{x:.1e}")) ax.set( xlim=(0, self.frames * self.interval / 1000), xlabel=self.axes_labels["time"], ) ax.grid(linestyle=":") self.ax[0].set(ylabel="i", xlabel="j") self.ax[1].set(ylabel=self.axes_labels["temp"]) self.ax[2].set(ylabel=self.axes_labels["field"]) def __init_ani_no_time_series(self): self.__set_axes_no_time_series() self.ax[0].imshow(self.lattice.state, norm=Normalize(vmin=-1.0, vmax=1.0)) def __update_ani_no_time_series(self, frame): for ax in self.ax: ax.clear() self.update() self.__set_axes_no_time_series() self.fig.suptitle(self.__str__()) self.ax[0].imshow(self.lattice.state, norm=Normalize(vmin=-1.0, vmax=1.0)) self.ax[1].plot(self.time_hist, self.temp_hist, color="purple") self.ax[2].plot(self.time_hist, self.field_hist, color="purple")Ancestors
Instance variables
var time-
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@property def time(self): return self.gen * self.interval / 1000
Methods
def update(self)-
Updates the system to the next generation, appending new values to the history list of each phisical quantity. This function is automatically called by the animation attribute to render the next frame.
Expand source code
def update(self): """ Updates the system to the next generation, appending new values to the history list of each phisical quantity. This function is automatically called by the animation attribute to render the next frame. """ self.temp = self.temp_func(self.time) self.field = self.field_func(self.time) super().update() self.time_hist.append(self.time) self.temp_hist.append(self.temp) self.field_hist.append(self.field)
class Ising (shape=(128, 128), temp=2.0, j=(1.0, 1.0), field=0.0, init_state='random')-
The core implementation of the Ising Model. No animation here.
Args
shape:2-tupleofints; Default is (128, 128)- the shape of the lattice of spins.
temp:float; Default is 2.0- the initial temperature of the lattice as a whole.
j:floator2-tupleoffloats; Default is 1.0- the coefficient of interaction between neighboring spins in the lattice. when a tuple is suplied, the first value is the coefficient for row neighbors and the second value is the coefficient for column neighbors.
field:float; Default is 0.0- the initial value for the external magnetic field.
init_state:{"random", "down", "up"}; Default is "random"- the initial configuration of the spins in the lattice.
Attributes
gen:int- the current generation of the system. Starts at 0 and is incremented by a call to update method
init_state:{"random", "down", "up"}; Default is "random"- the initial configuration of the spins in the lattice.
spins:int- the number of the spins in the lattice
lattice:Lattice- an instance of a Lattice object that describes the current state of the system
temp:float- the current temperature of the lattice, in energy units. A new value can be assigned anytime.
field:float- the current value of the external magnetic field, oriented perpendicularlly to the lattice. A positive value represents a up oriented field. A new value can be assigned anytime.
energy:float- the total energy of the lattice in its current generation.
mag_mom:float- the total magnetic moment of the lattice in its current generation.
mean_energy_hist:list[float]- a list with the values of the mean energy for each past generation. New values are appended by a call to the update function
magnet_hist:list[float]- a list with the values of the magnetization per spin for each past generation. New values are appended by a call to the update function
specific_heat_hist:list[float]- a list with the values of the specific heat per spin for each past generation. New values are appended by a call to the update function
susceptibility_hist:list[float]- a list with the values of the magnetic susceptibility for each past generation. New values are appended by a call to the update function
Expand source code
class Ising: """ The core implementation of the Ising Model. No animation here. Args ------------------ shape : 2-tuple of ints; Default is (128, 128) the shape of the lattice of spins. temp : float; Default is 2.0 the initial temperature of the lattice as a whole. j : float or 2-tuple of floats; Default is 1.0 the coefficient of interaction between neighboring spins in the lattice. when a tuple is suplied, the first value is the coefficient for row neighbors and the second value is the coefficient for column neighbors. field : float; Default is 0.0 the initial value for the external magnetic field. init_state : {"random", "down", "up"}; Default is "random" the initial configuration of the spins in the lattice. Attributes ------------------ gen : int the current generation of the system. Starts at 0 and is incremented by a call to update method init_state : {"random", "down", "up"}; Default is "random" the initial configuration of the spins in the lattice. spins : int the number of the spins in the lattice lattice : Lattice an instance of a Lattice object that describes the current state of the system temp : float the current temperature of the lattice, in energy units. A new value can be assigned anytime. field : float the current value of the external magnetic field, oriented perpendicularlly to the lattice. A positive value represents a up oriented field. A new value can be assigned anytime. energy : float the total energy of the lattice in its current generation. mag_mom : float the total magnetic moment of the lattice in its current generation. mean_energy_hist : list[float] a list with the values of the mean energy for each past generation. New values are appended by a call to the update function magnet_hist : list[float] a list with the values of the magnetization per spin for each past generation. New values are appended by a call to the update function specific_heat_hist : list[float] a list with the values of the specific heat per spin for each past generation. New values are appended by a call to the update function susceptibility_hist : list[float] a list with the values of the magnetic susceptibility for each past generation. New values are appended by a call to the update function """ def __init__( self, shape=(128, 128), temp=2.0, j=(1.0, 1.0), field=0.0, init_state="random", ) -> None: # Saving given init_state to include in __str__ if init_state == "up": self._init_state = "up" elif init_state == "down": self._init_state = "down" else: self._init_state = "random" self.lattice = Lattice(shape, temp, j, field, init_state) self._energy = self.lattice.energy self._mag_mom = self.lattice.mag_mom self.mean_energy_hist = [self.lattice.mean_energy()] self.magnet_hist = [self.lattice.magnet() / self.spins] self.specific_heat_hist = [0.0] self.susceptibility_hist = [0.0] def __repr__(self) -> str: return ( f"Ising(shape={self.lattice.shape.__str__()}, " + f"temp={self.lattice.temp}, " + f"j={self.lattice.j.__str__()}, " + f"field={self.lattice.field})" ) def __str__(self) -> str: return ( f"Ising Model with Temperature {self.lattice.temp:.2f} and Field {self.lattice.field:.2f}, " + f"starting with {self.init_state} spins" ) @property def spins(self): return self.lattice.spins @property def init_state(self): return self._init_state @property def gen(self): return self.lattice._gen @property def temp(self): return self.lattice.temp @temp.setter def temp(self, value): self.lattice.temp = value @property def field(self): return self.lattice.field @field.setter def field(self, value): self.lattice.field = value @property def energy(self): return self.lattice.energy @property def mag_mom(self): return self.lattice.mag_mom def update(self): """ Updates the system to the next generation, appending new values to the history list of each phisical quantity. """ self.lattice.update() self.mean_energy_hist.append(self.lattice.mean_energy()) self.magnet_hist.append(self.lattice.magnet() / self.spins) self.specific_heat_hist.append(self.lattice.specific_heat() / self.spins) self.susceptibility_hist.append(self.lattice.susceptibility())Subclasses
Instance variables
var energy-
Expand source code
@property def energy(self): return self.lattice.energy var field-
Expand source code
@property def field(self): return self.lattice.field var gen-
Expand source code
@property def gen(self): return self.lattice._gen var init_state-
Expand source code
@property def init_state(self): return self._init_state var mag_mom-
Expand source code
@property def mag_mom(self): return self.lattice.mag_mom var spins-
Expand source code
@property def spins(self): return self.lattice.spins var temp-
Expand source code
@property def temp(self): return self.lattice.temp
Methods
def update(self)-
Updates the system to the next generation, appending new values to the history list of each phisical quantity.
Expand source code
def update(self): """ Updates the system to the next generation, appending new values to the history list of each phisical quantity. """ self.lattice.update() self.mean_energy_hist.append(self.lattice.mean_energy()) self.magnet_hist.append(self.lattice.magnet() / self.spins) self.specific_heat_hist.append(self.lattice.specific_heat() / self.spins) self.susceptibility_hist.append(self.lattice.susceptibility())