Heat bath 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 = 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
beta = 1.0
S = [random.choice([-1, 1]) for site 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
random.seed('123456')
for step in range(nsteps):
k = random.randint(0, N - 1)
Upsilon = random.uniform(0.0, 1.0)
h = sum(S[nn] for nn in nbr[k])
Sk_old = S[k]
S[k] = -1
if Upsilon < 1.0 / (1.0 + math.exp(-2.0 * beta * h)):
S[k] = 1
if S[k] != Sk_old:
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)
