Ising mean field 1d.py

From Werner KRAUTH

This is the Python program which computes the self-consistent solution for a one-dimensional chain of Ising spins, where we put the spin at k=0 equal to 1. Two following approaches are used: On the one hand the true self-consistency, and on the other the linearized version.

import math, numpy, pylab

length = 100
m_vec = [0] * (length + 1)
x_vec = range(length)
m_vec[0] = 1.0
Tc = 2.0
t_vec = [0.0025, 0.01, 0.04, 0.16]
for t in t_vec:
    beta = (t * Tc + Tc) ** (-1)
    for iter in range(100000):
        for i in range(1, length):
            m_vec[i] =  beta * (m_vec[i - 1] + m_vec[i + 1])
    pylab.semilogy(x_vec, m_vec[0: length],label='lin' + str(t))
    for iter in range(100000):
        for i in range(1, length):
            m_vec[i] = math.tanh( beta * (m_vec[i - 1] + m_vec[i + 1]))
    pylab.semilogy(x_vec, m_vec[0:length],label='th' + str(t))
pylab.title('Mean-field self-consistency 1-d Ising model, $m(0)=1$, $m(L) = 0$')
pylab.xlabel('$k$ (Lattice sites) ', fontsize=18)
pylab.ylabel('$m(0)m(k)$ (Mean-field correlation)', fontsize=18)
pylab.legend(loc='lower left')
pylab.savefig('mean_field_1d_Ising.png')
pylab.show()