A Comment on the beta-expansion of s=1/2 and s=1 Ising Models

TL;DR

This paper applies a new formalism to derive analytical beta-expansions for thermodynamic functions in spin-1 and spin-1/2 Ising chains, comparing their convergence properties.

Contribution

It demonstrates how to obtain beta-expansions without solving transfer matrix equations and compares convergence issues between different spin models.

Findings

Beta-expansions are less convergent when auxiliary functions have singularities.

The method avoids solving transfer matrix equations.

Comparison of thermodynamic properties between s=1/2 and s=1 models.

Abstract

The purpose of the present work is to apply the method recently developed in reference [chain_m] to the spin-1 Ising chain, showing how to obtain analytical $\beta$-expansions of thermodynamical functions through this formalism. In this method, we do not solve any transfer matrix-like equations. A comparison between the $\beta$-expansions of the specific heat and the magnetic susceptibility for the $s=1/2$ and $s=1$ one-dimensional Ising models is presented. We show that those expansions have poorer convergence when the auxiliary function of the model has singularities.