From Werner KRAUTH

Revision as of 21:51, 22 September 2015 Werner (Talk | contribs) ← Previous diff		Revision as of 22:24, 4 March 2024 Werner (Talk | contribs) (→Program) Next diff →
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	=Program=		=Program=
		+	import random, math
-		+	L = 6
-		+
-		+
-	import random, math	+
-		+
-	L = 16	+
	N = L * L		N = L * L
	nbr = {i : ((i // L) * L + (i + 1) % L, (i + L) % N,		nbr = {i : ((i // L) * L + (i + 1) % L, (i + L) % N,
	(i // L) * L + (i - 1) % L, (i - L) % N) \		(i // L) * L + (i - 1) % L, (i - L) % N) \
	for i in range(N)}		for i in range(N)}
-	nsteps = 1000000	+	nsteps = 10000000
-	T = 2.0	+	T = 1.0
	beta = 1.0 / T		beta = 1.0 / T
	S = [random.choice([1, -1]) for k in range(N)]		S = [random.choice([1, -1]) for k in range(N)]
		+	E = -0.5 * sum(S[k] * sum(S[nn] for nn in nbr[k]) \
		+	for k in range(N))
		+	E_tot, E2_tot = 0.0, 0.0
	for step in range(nsteps):		for step in range(nsteps):
	k = random.randint(0, N - 1)		k = random.randint(0, N - 1)
-	delta_E = 2.0 * S[k] * sum(S[nn] for nn in nbr[k])	+	h = sum(S[nn] for nn in nbr[k])
		+	Sk_old = S[k]
		+	delta_E = 2.0 * S[k] * h
	if random.uniform(0.0, 1.0) < math.exp(-beta * delta_E):		if random.uniform(0.0, 1.0) < math.exp(-beta * delta_E):
	S[k] *= -1		S[k] *= -1
-	print S, sum(S)	+	E -= 2.0 * h * S[k]
		+	E_tot += E
		+	E2_tot += E ** 2
		+	E_av = E_tot / float(nsteps)
		+	E2_av = E2_tot / float(nsteps)
		+	c_V = beta ** 2 * (E2_av - E_av ** 2) / float(N)
		+	print(E_av / N,c_V)
	=Version=		=Version=

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Revision as of 22:24, 4 March 2024

This page presents the program markov_ising.py, a Markov-chain algorithm for the Ising model on an LXL square lattice in two dimensions.

Contents 1 Description 2 Program 3 Version

Description

Program

import random, math

L = 6
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)}
nsteps = 10000000
T = 1.0
beta = 1.0 / T
S = [random.choice([1, -1]) for k in range(N)]
E = -0.5 * sum(S[k] * sum(S[nn] for nn in nbr[k]) \
                                for k in range(N))
E_tot, E2_tot = 0.0, 0.0
for step in range(nsteps):
    k = random.randint(0, N - 1)
    h = sum(S[nn] for nn in nbr[k])
    Sk_old = S[k]
    delta_E = 2.0 * S[k] * h
    if random.uniform(0.0, 1.0) < math.exp(-beta * delta_E):
        S[k] *= -1
        E -= 2.0 * h * S[k]
    E_tot += E
    E2_tot += E ** 2
E_av  = E_tot / float(nsteps)
E2_av = E2_tot / float(nsteps)
c_V = beta ** 2 * (E2_av - E_av ** 2) / float(N)
print(E_av / N,c_V)

Version

See history for version information.