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Welcome to the website for Pathria, Beale: Statistical Mechanics, 3rd Edition.


Statistical Mechanics

This site consists of Mathematica Files, and Errata.


Mathematica Files


Exact calculation of the partition function of the two-dimensional Ising model on an n × m square lattice.

This Mathematica code calculates the exact partition function of the two-dimensional Ising model on an n × m square lattice with periodic boundary conditions. Copyright : Paul D.Beale,2010.

The code is based on:

Paul D. Beale, Phys. Rev. Lett. 76, 78 (1996),
and Section 13.4.A of
R.K. Pathria and Paul D. Beale, Statistical Mechanics, Third Edition (Academic, Boston, 2011).

The user's input parameters are two positive integers n and m specifying the numbers of rows and columns of the square lattice. The code has been tested on lattice sizes up to 128 × 128.

The code calculates:

z = Sum[g[[q + 1]] x^(2 q), {q, 0, n m}] = partition function defined in
Pathria and Beale, equation 13.4.57 or 13.4.58

g[[q + 1]] = partitionfunction coefficient which gives the number microconfigurations with
energy 4qJ above the ground state.

x = Exp[-2 K] is the Boltzmann factor for a single spin flip where K=J/kT

s[[q + 1]]=Log[g[[q+1]]]= microcanonical entropy for energy 4qJ above the ground state.
The valueof s=-∞ for some values of q since there are no states with that energy.

This code may be used for noncommercial purposes by referencing:

Paul D. Beale, Phys. Rev. Lett. 76, 78 (1996),
and
R.K. Pathria and Paul D. Beale, Statistical Mechanics, Third Edition (Academic, Boston, 2011).

Input n and m:

n is the number of rows and m is the number of columns.
The case n=1 (or m=1) gives the one-dimensional Ising model.


Errata - Updated July 2012


  • Errata


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