New Algorithm of the Finite Lattice Method for the High-temperature Expansion of the Ising Model in Three Dimensions

TL;DR

This paper introduces a new finite lattice method algorithm that significantly extends the high-temperature series for the 3D Ising model, enabling more precise estimates of critical exponents.

Contribution

A novel finite lattice method algorithm that extends the high-temperature series for the 3D Ising model from 26th to 46th order.

Findings

Extended series improve critical exponent estimates

Series up to 46th order achieved

Enhanced precision in high-temperature expansion

Abstract

We propose a new algorithm of the finite lattice method to generate the high-temperature series for the Ising model in three dimensions. It enables us to extend the series for the free energy of the simple cubic lattice from the previous series of 26th order to 46th order in the inverse temperature. The obtained series give the estimate of the critical exponent for the specific heat in high precision.