From Werner KRAUTH

Revision as of 07:52, 22 February 2023 Werner (Talk | contribs) (→Program (in Python3) ← Previous diff		Current revision Werner (Talk | contribs)
Line 20:		Line 20:
	S1 = [-1] * N		S1 = [-1] * N
	S2 = [1] * N		S2 = [1] * N
-	nsteps = 10000
	step = 0		step = 0
	while True:		while True:
Line 36:		Line 35:
	break		break
	print(T, MeanCoupling / NIter)		print(T, MeanCoupling / NIter)
		+	=Output=
		+	A slightly modified graphics version of this program produces the following output:
		+	[[Image:IsingCoupling.png|left|50px]]
		+	<br clear="all" />
	=Version=		=Version=
	See history for version information.		See history for version information.
	[[Category:Python]] [[Category:Honnef_2015]] [[Category:MOOC_SMAC]]		[[Category:Python]] [[Category:Honnef_2015]] [[Category:MOOC_SMAC]]

---

Current revision

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.

Contents 1 Description 2 Program (in Python3) 3 Output 4 Version

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.