From Werner KRAUTH

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	=Description=		=Description=
-	The program performs a most basic iteration (searching self-consistency) of the m = tanh(q beta m) loop.	+	The program performs a most basic iteration (searching self-consistency) of the m = tanh(q beta m) loop. If you run this program, you will notice the appearance of a self-consistent solution with m different from zero at temperatures below T=4.
	=Program=		=Program=

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Current revision

This page presents the Python2 program Mean_field_self_consistency_single_site.py, that obtains the most basic self-consistency solution for the Ising model.

Contents 1 Reference 2 Description 3 Program 4 Version

Reference

This program is discussed in Lecture 08 of my 2019 ICFP lecture on Statistical physics: "Mean-field theory: The three pillars".

Description

The program performs a most basic iteration (searching self-consistency) of the m = tanh(q beta m) loop. If you run this program, you will notice the appearance of a self-consistent solution with m different from zero at temperatures below T=4.

Program

import random, math, pylab

dim = 2
q = 2.0 * dim
Tc = 2.0 * dim
m_vec = [1.0]
T_vec = [0]
for iter in range(-1000, 1000):
    t = iter / float(1100.0)
    beta = (t * Tc + Tc) ** (-1)
    T_vec.append(1.0 / beta)
    m = 0.1
    for iter2 in range(1000):
        m = math.tanh(beta * q * m)
    m_vec.append(m)
pylab.plot(T_vec, m_vec)
pylab.title('Weiss self-consistency for the Ising model 
in $d$ = ' +  str(dim) + ' dimensions')
pylab.xlabel('$T$ (Temperature)', fontsize=18)
pylab.ylabel('$m$ (magnetization per site)', fontsize=18)
pylab.savefig('mean_field_self_consistency_Ising.png')
pylab.show()

Version

See history for version information.