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guanjihuan
2023-11-07 03:38:46 +08:00
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2019.12.01_simulation_of_Ising_model_with_Monte_Carlo_method/Ising_model.py Normal file
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"""
This code is supported by the website: https://www.guanjihuan.com
The newest version of this code is on the web page: https://www.guanjihuan.com/archives/1249
"""
import random
import matplotlib.pyplot as plt
import numpy as np
import copy
import math
import time
def main():
size = 30 # 体系大小
T = 2 # 温度
ising = get_one_sample(sizeOfSample=size, temperature=T) # 得到符合玻尔兹曼分布的ising模型
plot(ising) # 画图
energy_s = []
for i in range(size):
for j in range(size):
energy_s0 = getEnergy(i=i, j=j, S=ising) # 获取格点的能量
energy_s = np.append(energy_s, [energy_s0], axis=0)
plt.hist(energy_s, bins=50, density=1, facecolor='red', alpha=0.7) # 画出格点能量分布 # bins是分布柱子的个数，density是归一化，后面两个参数是管颜色的
plt.show()
def get_one_sample(sizeOfSample, temperature):
S = 2 * np.pi * np.random.random(size=(sizeOfSample, sizeOfSample)) # 随机初始状态，角度是0到2pi
print('体系大小：', S.shape)
initialEnergy = calculateAllEnergy(S) # 计算随机初始状态的能量
print('系统的初始能量是:', initialEnergy)
newS = np.array(copy.deepcopy(S))
for i00 in range(1000): # 循环一定次数，得到平衡的抽样分布
newS = Metropolis(newS, temperature) # Metropolis方法抽样，得到玻尔兹曼分布的样品体系
newEnergy = calculateAllEnergy(newS)
if np.mod(i00, 100) == 0:
print('循环次数%i, 当前系统能量是:' % (i00+1), newEnergy)
print('循环次数%i, 当前系统能量是:' % (i00 + 1), newEnergy)
return newS
def Metropolis(S, T): # S是输入的初始状态， T是温度
delta_max = 0.5 * np.pi # 角度最大的变化度数，默认是90度，也可以调整为其他
k = 1 # 玻尔兹曼常数
for i in range(S.shape[0]):
for j in range(S.shape[0]):
delta = (2 * np.random.random() - 1) * delta_max # 角度变化在-90度到90度之间
newAngle = S[i, j] + delta # 新角度
energyBefore = getEnergy(i=i, j=j, S=S, angle=None) # 获取该格点的能量
energyLater = getEnergy(i=i, j=j, S=S, angle=newAngle) # 获取格点变成新角度时的能量
alpha = min(1.0, math.exp(-(energyLater - energyBefore)/(k * T))) # 这个接受率对应的是玻尔兹曼分布
if random.uniform(0, 1) <= alpha:
S[i, j] = newAngle # 接受新状态
else:
pass # 保持为上一个状态
return S
def getEnergy(i, j, S, angle=None): # 计算(i,j)位置的能量，为周围四个的相互能之和
width = S.shape[0]
height = S.shape[1]
top_i = i - 1 if i > 0 else width - 1 # 用到周期性边界条件
bottom_i = i + 1 if i < (width - 1) else 0
left_j = j - 1 if j > 0 else height - 1
right_j = j + 1 if j < (height - 1) else 0
environment = [[top_i, j], [bottom_i, j], [i, left_j], [i, right_j]]
energy = 0
if angle == None:
for num_i in range(4):
energy += -np.cos(S[i, j] - S[environment[num_i][0], environment[num_i][1]])
else:
for num_i in range(4):
energy += -np.cos(angle - S[environment[num_i][0], environment[num_i][1]])
return energy
def calculateAllEnergy(S): # 计算整个体系的能量
energy = 0
for i in range(S.shape[0]):
for j in range(S.shape[1]):
energy += getEnergy(i, j, S)
return energy/2 # 作用两次要减半
def plot(S): # 画图
X, Y = np.meshgrid(np.arange(0, S.shape[0]), np.arange(0, S.shape[0]))
U = np.cos(S)
V = np.sin(S)
plt.figure()
plt.quiver(X, Y, U, V, units='inches')
plt.show()
if __name__ == '__main__':
main()

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2019.12.01_simulation_of_Ising_model_with_Monte_Carlo_method/get_the_transition_temperature_by_calculating_magnetic_moments_in_Ising_model.py Normal file
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"""
This code is supported by the website: https://www.guanjihuan.com
The newest version of this code is on the web page: https://www.guanjihuan.com/archives/1249
"""
import random
import matplotlib.pyplot as plt
import numpy as np
import copy
import math
import time
def main():
size = 30 # 体系大小
for T in np.linspace(0.02, 5, 100):
ising, magnetism = get_one_sample(sizeOfSample=size, temperature=T)
print('温度=', T, ' 磁矩=', magnetism, ' 总能量=', calculateAllEnergy(ising))
plt.plot(T, magnetism, 'o')
plt.show()
def get_one_sample(sizeOfSample, temperature):
newS = np.zeros((sizeOfSample, sizeOfSample)) # 初始状态
magnetism = 0
for i00 in range(100):
newS = Metropolis(newS, temperature)
magnetism = magnetism + abs(sum(sum(np.cos(newS))))/newS.shape[0]**2
magnetism = magnetism/100
return newS, magnetism
def Metropolis(S, T): # S是输入的初始状态， T是温度
k = 1 # 玻尔兹曼常数
for i in range(S.shape[0]):
for j in range(S.shape[0]):
newAngle = np.random.randint(-1, 1)*np.pi
energyBefore = getEnergy(i=i, j=j, S=S, angle=None) # 获取该格点的能量
energyLater = getEnergy(i=i, j=j, S=S, angle=newAngle) # 获取格点变成新角度时的能量
alpha = min(1.0, math.exp(-(energyLater - energyBefore)/(k * T))) # 这个接受率对应的是玻尔兹曼分布
if random.uniform(0, 1) <= alpha:
S[i, j] = newAngle # 接受新状态
else:
pass # 保持为上一个状态
return S
def getEnergy(i, j, S, angle=None): # 计算(i,j)位置的能量，为周围四个的相互能之和
width = S.shape[0]
height = S.shape[1]
top_i = i - 1 if i > 0 else width - 1 # 用到周期性边界条件
bottom_i = i + 1 if i < (width - 1) else 0
left_j = j - 1 if j > 0 else height - 1
right_j = j + 1 if j < (height - 1) else 0
environment = [[top_i, j], [bottom_i, j], [i, left_j], [i, right_j]]
energy = 0
if angle == None:
for num_i in range(4):
energy += -np.cos(S[i, j] - S[environment[num_i][0], environment[num_i][1]])
else:
for num_i in range(4):
energy += -np.cos(angle - S[environment[num_i][0], environment[num_i][1]])
return energy
def calculateAllEnergy(S): # 计算整个体系的能量
energy = 0
for i in range(S.shape[0]):
for j in range(S.shape[1]):
energy += getEnergy(i, j, S)
return energy/2 # 作用两次要减半
if __name__ == '__main__':
main()