Ising coupling.py

From Werner KRAUTH

Context

This page is part of my 2024 Beg Rohu Lectures on "The second Markov chain revolution" at the Summer School "Concepts and Methods of Statistical Physics" (3 - 15 June 2024).

Python program

import math
import random
 
L = 64; 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)}
beta = 0.4  #  beta = 0.4407 is critical temperature
SLow = [-1 for site in range(N)]
SHigh = [1 for site in range(N)]
iter = 0
while True:
    iter += 1
    k = random.randint(0, N - 1)
    Upsilon = random.uniform(0.0, 1.0)
    hLow = sum(SLow[nn] for nn in nbr[k])
    hHigh = sum(SHigh[nn] for nn in nbr[k])
    SLow[k] = -1
    if Upsilon < 1.0 / (1.0 + math.exp(-2.0 * beta * hLow)):
        SLow[k] = 1
    SHigh[k] = -1
    if Upsilon < 1.0 / (1.0 + math.exp(-2.0 * beta * hHigh)):
        SHigh[k] = 1
    if SHigh == SLow:
        print(iter / N)
        print(SLow, SHigh)
        break