Partition Function for Two-Dimensional Nearest Neighbour Ising Model in a Non-Zero Magnetic Field for a Square Lattice of 16 Sites

TL;DR

This paper derives an explicit partition function for a 2D Ising model with a magnetic field on a 16-site square lattice, confirming critical temperature accuracy and estimating magnetic field strength.

Contribution

It provides a systematic enumeration method to explicitly compute the partition function for a small 2D Ising lattice with magnetic field, a novel explicit calculation.

Findings

Critical temperature matches reported values

Magnetic field dimensionless value is 0.004

Method confirms accuracy of known critical points

Abstract

An explicit expression for the partition function of two-dimensional nearest neighbour Ising models in the presence of a magnetic field is derived by a systematic enumeration of all the spin configurations pertaining to a square lattice of sixteen sites. The critical temperature is shown to be in excellent agreement with the reported values while the corresponding dimensionless magnetic field is obtained as 0.004.