Enumerate 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]] | ||
+ | |||
+ | |||
def gray_flip(t, N): | def gray_flip(t, N): | ||
k = t[0] | k = t[0] |
Revision as of 21:39, 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.
def gray_flip(t, N): k = t[0] if k > N: return t, k t[k - 1] = t[k] t[k] = k + 1 if k != 1: t[0] = 1 return t, k L = 4 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)} S = [-1] * N E = -2 * N print S, E tau = range(1, N + 2) for i in range(1, 2 ** N): tau, k = gray_flip(tau, N) h = sum(S[n] for n in nbr[k - 1]) E += 2 * h * S[k - 1] S[k - 1] *= -1 print S, E