Heat bath ising.py

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 21:37, 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

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)
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