From Werner KRAUTH

This page presents the program coupling_ising.py, a heat-bath algorithm for the Ising model on an LxL square lattice in two dimensions, run for two configurations at a time. The algorithm illustrates the coupling phenomenon.

Description

Program (in Python3)

import random, math

L = 7
N = L * L
nbr = {i : ((i // L) * L + (i + 1) % L, (i + L) % N,
            (i // L) * L + (i - 1) % L, (i - L) % N) \
                                    for i in range(N)}
NIter = 100
for TT in range(20, 40):
    T = TT / 10
    beta = 1.0 / T
    MeanCoupling = 0
    for iter in range(NIter):
        S1 = [-1] * N
        S2 = [1] * N
        step = 0
        while True:
            step += 1
            k = random.randint(0, N - 1)
            Upsilon = random.uniform(0.0, 1.0)
            h1 = sum(S1[nn] for nn in nbr[k])
            S1[k] = -1
            if Upsilon < 1.0 / (1.0 + math.exp(-2.0 * beta * h1)): S1[k] = 1
            h2 = sum(S2[nn] for nn in nbr[k])
            S2[k] = -1
            if Upsilon < 1.0 / (1.0 + math.exp(-2.0 * beta * h2)): S2[k] = 1
            if S1 == S2:
                MeanCoupling += step
                break
    print(T, MeanCoupling / NIter)

Output

A slightly modified graphics version of this program produces the following output:

Version

See history for version information.