Mean field self consistency single site.py
From Werner KRAUTH
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- | 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= |
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 |
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Reference
This program is discussed in Lecture 08 of my 2019 ICFP lecture on Statistical physics: "Mean-field theory: The three pillars".
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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.
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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()
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Version
See history for version information.
Categories: Python | ICFP