From Werner KRAUTH

Revision as of 10:59, 8 November 2016 Werner (Talk | contribs) ← Previous diff		Current revision Werner (Talk | contribs) (→Description)
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		+	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.
		+
		+	__FORCETOC__
		+	=Reference=
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		+	This program is discussed in [[ICFP_Stat_Physics_2019|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		import random, math, pylab
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	pylab.savefig('mean_field_self_consistency_Ising.png')		pylab.savefig('mean_field_self_consistency_Ising.png')
	pylab.show()		pylab.show()
		+
		+	=Version=
		+	See history for version information.
		+
		+	[[Category:Python]] [[Category:ICFP]]

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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.