From Werner KRAUTH

This page presents the program markov_disks_box.py, a Markov-chain algorithm for four disks in a square box of sides 1.

Contents 1 Description 2 Program 3 Version

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 math, os 

L = 6
N = L * L
filename = 'data_dos_L%i.txt' % L
if os.path.isfile(filename):
    dos = {}
    f = open(filename, 'r')
    for line in f:
        E, N_E = line.split()
        dos[int(E)] = int(N_E)
    f.close()
else:
   exit('input file missing')
list_T = [0.5 + 0.5 * i for i in range(10)]
for T in list_T:
    Z = 0.0
    E_av = 0.0
    M_av = 0.0
    E2_av = 0.0
    for E in dos.keys():
        weight = math.exp(- E / T) * dos[E]
        Z += weight
        E_av += weight * E
        E2_av += weight * E ** 2
    E2_av /= Z
    E_av /= Z
    cv = (E2_av - E_av ** 2) / N / T ** 2
    print T, E_av / float(N), cv