Coupling ising.py
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.
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Description
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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)
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Output
A slightly modified graphics version of this program produces the following output:
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Version
See history for version information.