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. | + | This page presents the program heat_bath_ising.py, a heat-bath algorithm for the Ising model on an LxL square lattice in two dimensions. |
__FORCETOC__ | __FORCETOC__ | ||
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=Program= | =Program= | ||
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- | import random | ||
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- | 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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import random, math | import random, math | ||
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E2_av = E2_tot / float(nsteps) | E2_av = E2_tot / float(nsteps) | ||
c_V = beta ** 2 * (E2_av - E_av ** 2) / float(N) | c_V = beta ** 2 * (E2_av - E_av ** 2) / float(N) | ||
+ | =Version= | ||
+ | See history for version information. | ||
+ | |||
+ | [[Category:Python]] |
Revision as of 21:47, 22 September 2015
This page presents the program heat_bath_ising.py, a heat-bath algorithm for the Ising model on an LxL square lattice in two dimensions.
Contents |
Description
Program
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)
Version
See history for version information.