# Enumerate ising dos.py

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.

# 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)".

# 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.

# 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]
```

# Version

See history for version information.