Markov 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. | + | This page presents the program markov_ising.py, a Markov-chain algorithm for the Ising model on an LXL square lattice in two dimensions. |
- | + | ||
__FORCETOC__ | __FORCETOC__ | ||
=Description= | =Description= | ||
Line 6: | Line 5: | ||
=Program= | =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]] | ||
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S[k] *= -1 | S[k] *= -1 | ||
print S, sum(S) | print S, sum(S) | ||
+ | |||
+ | =Version= | ||
+ | See history for version information. | ||
+ | |||
+ | [[Category:Python]] [[Category:Honnef_2015]] [[Category:MOOC_SMAC]] |
Revision as of 21:51, 22 September 2015
This page presents the program markov_ising.py, a Markov-chain algorithm for the Ising model on an LXL square lattice in two dimensions.
Contents |
Description
Program
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)
Version
See history for version information.