Enumerate ising dos.py

From Werner KRAUTH

This page presents the program Enumerate_ising_dos.py, the enumeration of the Ising-model configurations for small lattices (see also the simpler version of the program). Periodic boundary conditions are supposed.

1 Reference
2 Description
3 Program
4 Version

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Reference

W. Krauth Statistical Mechanics: Algorithms and Computations Oxford University Press (2006) This program is discussed in Lecture 3 of my ICFP course 2015 on Statistical physics. The Lectures is called "Exact computations in the two-dimensional Ising model (Kac-Ward)".

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Description

This program uses a Gray-code enumeration to go through all the configurations of the Ising model on square lattices of width L with periodic boundary conditions.

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Program

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
dos = {}
dos[E] = 1
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
    if E in dos: dos[E] += 1
    else:        dos[E] = 1
for E in sorted(dos.keys()):
    print E, dos[E]

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