Cluster ising.py
From Werner KRAUTH
This page presents the program markov_disks_box.py, a Markov-chain algorithm for four disks in a square box of sides 1.
Contents |
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 = 100
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)}
T = 2.5
p = 1.0 - math.exp(-2.0 / T)
nsteps = 10000
S = [random.choice([1, -1]) for k in range(N)]
for step in range(nsteps):
k = random.randint(0, N - 1)
Pocket, Cluster = [k], [k]
while Pocket != []:
j = random.choice(Pocket)
for l in nbr[j]:
if S[l] == S[j] and l not in Cluster \
and random.uniform(0.0, 1.0) < p:
Pocket.append(l)
Cluster.append(l)
Pocket.remove(j)
for j in Cluster:
S[j] *= -1
