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=
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=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.

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