New algorithm of the high-temperature expansion for the Ising model in three dimensions

TL;DR

This paper introduces a novel algorithm for the high-temperature expansion of the 3D Ising model, significantly extending the series length compared to previous methods, thus enabling more precise analysis of the model.

Contribution

A new finite lattice method algorithm that produces longer high-temperature series for the 3D Ising model than existing algorithms and the standard graphical method.

Findings

Extended the series for free energy from beta^{26} to beta^{46}.

Extended the series for magnetic susceptibility from beta^{25} to beta^{32}.

Demonstrated improved efficiency and longer series generation.

Abstract

New algorithm of the finite lattice method is presented to generate the high-temperature expansion series of the Ising model. It enables us to obtain much longer series in three dimensions when compared not only to the previous algorithm of the finite lattice method but also to the standard graphical method. It is applied to extend the high-temperature series of the simple cubic Ising model from beta^{26} to beta^{46} for the free energy and from beta^{25} to beta^{32} for the magnetic susceptibility.