Propp-Wilson/grid_clusterd.py at master · Teiolass/Propp-Wilson · GitHub

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
import numpy as np
import numpy.random as rnd
from collections import deque
import matplotlib.pyplot as plt


N = 25
beta = 0
beta_step = 0.02
times = 40


class Random_gen:
    def __init__(self, N):
        self.nmax = N * N * 2
        self.depth = 0
        self.rarr = np.zeros((0,), dtype=float)
        self.narr = np.zeros((0), dtype=int)

    def advance_depth(self, nd):
        self.rarr.resize((nd,), refcheck=False)
        self.narr.resize((nd,), refcheck=False)
        self.rarr[self.depth:] = rnd.random((nd-self.depth,))
        self.narr[self.depth:] = rnd.randint(0, self.nmax, size=(nd-self.depth,))
        self.depth = nd

def are_in_same_cc(V, x1, x2):
    que = deque()
    x = x1
    N = V.shape[0]
    adj = [(1,0,0),(0,1,1),(-1,0,0),(0,-1,1)]
    visited = np.zeros((N,N), dtype=bool)
    visited[x] = True
    while len(que) > 0:
        x = que.popleft()
        if x == x2:
            return True
        visited[x] = True
        (i,j) = x
        if i+1 < N and V[i,j,0] == 1 and visited[i+1, j] == 0:
            que.append((i+1, j))
        if j+1 < N and V[i,j,1] == 1 and visited[i, j+1] == 0:
            que.append((i, j+1))
        if i > 0 and V[i-1,j,0] == 1 and visited[i-1, j] == 0:
            que.append((i-1, j))
        if j > 0 and V[i,j-1,1] == 1 and visited[i, j-1] == 0:
            que.append((i, j-1))
    return False

def multiple_step(p, V, narr, rarr):
    depth = rarr.size
    N = V.shape[0]
    for i in range(depth):
        index = depth - i - 1
        u = rarr[index]
        x = narr[index]
        i = x % N
        x = x // N
        j = x % N
        x = x // N
        d = x % 2
        e = (i,j,d)
        th1 = p / (2-p)
        if d == 0:
            y1 = 1
            y2 = 0
        else:
            y1 = 0
            y2 = 1
        x2 = ((i+y1)%N, (j+y2)%N)
        x1 = (i,j)
        V[i,j,d] = 0
        if u < th1:
            V[i,j,d] = 1
        elif u < p and are_in_same_cc(V, x1, x2):
            V[i,j,d] = 1

def get_clustered(N, p):
    depth = 1
    ran = Random_gen(N)
    ran.advance_depth(depth)
    while True:
        up = np.ones((N,N,2), dtype=bool)
        down = np.zeros((N,N,2), dtype=bool)
        multiple_step(p, up, ran.narr, ran.rarr)
        multiple_step(p, down, ran.narr, ran.rarr)
        if np.array_equal(up, down):
            break
        else:
            depth = max(depth+1, depth*2)
            ran.advance_depth(depth)
    return up

def get_ising(N, beta):
    p = (1 - np.exp(-beta*2))
    V = get_clustered(N, p)
    M = np.zeros((N,N), dtype=int)
    for i in range(N):
        for j in range(N):
            if M[i,j] != 0:
                continue
            sigma = rnd.randint(0,2) * 2 - 1
            que = deque()
            que.append((i,j))
            while len(que) > 0:
                i,j = que.popleft()
                M[i,j] = sigma
                if i+1 < N and V[i,j,0] == 1 and M[i+1, j] == 0:
                    que.append((i+1, j))
                if j+1 < N and V[i,j,1] == 1 and M[i, j+1] == 0:
                    que.append((i, j+1))
                if i > 0 and V[i-1,j,0] == 1 and M[i-1, j] == 0:
                    que.append((i-1, j))
                if j > 0 and V[i,j-1,1] == 1 and M[i, j-1] == 0:
                    que.append((i, j-1))
    return M

color_fore = '#A64444'
color_back = '#F2A66340'

plt.axis([0, 0.8, 0, 1])
plt.grid(True)

while beta <= 0.8:
    sm = 0
    beta += beta_step
    for _ in range(times):
        mag = np.abs(np.sum(get_ising(N, beta)) / (N*N))
        sm += mag
        plt.scatter(beta, mag, c=color_back, marker='.')
        plt.pause(0.001)
    sm /= times
    plt.scatter(beta, sm, c=color_fore, marker='o')
    plt.pause(0.001)

plt.show()