Enumerate ising.py

From Werner KRAUTH

This page presents the Python3 program enumerate_ising.py, an enumeration algorithm for the Ising model using the Gray code, on the two-dimensional L x L lattice with periodic boundary conditions. As it stands, the program is only really suited for L=2 and L=4. As Python is a bit slow, it will take a few hours to terminate for L=6.

1 Description
2 Program
3 Version

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Description

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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
print S, E
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
    print(S, E)

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