New algorithm for the computation of the partition function for the Ising model on a square lattice

TL;DR

This paper introduces a new efficient algorithm for calculating the partition function of the Ising model on a square lattice, significantly reducing computation time and aligning well with simulations and experiments.

Contribution

The paper presents a novel algorithm that drastically improves the efficiency of partition function computation for the Ising model on square lattices.

Findings

Reduces computation time by nine orders of magnitude for an 8x8 lattice.

Produces results that agree qualitatively with Monte Carlo simulations.

Outperforms mean field approach results in accuracy.

Abstract

A new and efficient algorithm is presented for the calculation of the partition function in the $S=\pm 1$ Ising model. As an example, we use the algorithm to obtain the thermal dependence of the magnetic spin susceptibility of an Ising antiferromagnet for a $8\times 8$ square lattice with open boundary conditions. The results agree qualitatively with the prediction of the Monte Carlo simulations and with experimental data and they are better than the mean field approach results. For the $8\times 8$ lattice, the algorithm reduces the computation time by nine orders of magnitude.