From Werner KRAUTH

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		+	This page presents the program markov_disks_box.py, a Markov-chain algorithm for four disks in a square box of sides 1.
		+
		+	__FORCETOC__
		+	=Description=
		+
		+	=Program=
		+
		+	import random
		+
		+	L = [[0.25, 0.25], [0.75, 0.25], [0.25, 0.75], [0.75, 0.75]]
		+	sigma = 0.15
		+	sigma_sq = sigma ** 2
		+	delta = 0.1
		+	n_steps = 1000
		+	for steps in range(n_steps):
		+	a = random.choice(L)
		+	b = [a[0] + random.uniform(-delta, delta), a[1] + random.uniform(-delta, delta)]
		+	min_dist = min((b[0] - c[0]) ** 2 + (b[1] - c[1]) ** 2 for c in L if c != a)
		+	box_cond = min(b[0], b[1]) < sigma or max(b[0], b[1]) > 1.0 - sigma
		+	if not (box_cond or min_dist < 4.0 * sigma ** 2):
		+	a[:] = b
		+	print L
		+
		+	=Version=
		+	See history for version information.
		+
		+	[[Category:Python]]
		+
		+
		+
	import random, math		import random, math

---

Revision as of 21:38, 22 September 2015

This page presents the program markov_disks_box.py, a Markov-chain algorithm for four disks in a square box of sides 1.

Contents 1 Description 2 Program 3 Version

Description

Program

import random

L = [[0.25, 0.25], [0.75, 0.25], [0.25, 0.75], [0.75, 0.75]]
sigma = 0.15
sigma_sq = sigma ** 2
delta = 0.1
n_steps = 1000
for steps in range(n_steps):
    a = random.choice(L)
    b = [a[0] + random.uniform(-delta, delta), a[1] + random.uniform(-delta, delta)]
    min_dist = min((b[0] - c[0]) ** 2 + (b[1] - c[1]) ** 2 for c in L if c != a)
    box_cond = min(b[0], b[1]) < sigma or max(b[0], b[1]) > 1.0 - sigma
    if not (box_cond or min_dist < 4.0 * sigma ** 2):
        a[:] = b
print L

Version

See history for version information.

import random, math

L = 16
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 = 1000000
T = 2.0
beta = 1.0 / T
S = [random.choice([1, -1]) for k in range(N)]
for step in range(nsteps):
    k = random.randint(0, N - 1)
    delta_E = 2.0 * S[k] * sum(S[nn] for nn in nbr[k])
    if random.uniform(0.0, 1.0) < math.exp(-beta * delta_E):
        S[k] *= -1
print S, sum(S)