Critical parameters and universal amplitude ratios of two-dimensional spin-S Ising models using high- and low-temperature expansions

TL;DR

This paper combines high- and low-temperature expansions to accurately determine critical parameters and verify universality in two-dimensional spin-S Ising models across various lattices.

Contribution

It introduces the first comprehensive calculation of critical parameters for general spin S Ising models using combined expansion methods and confirms universality of critical exponents and amplitude ratios.

Findings

Verified spin S independence of critical exponents and amplitude ratios

Provided estimates of critical amplitudes for multiple lattice types

Improved accuracy of critical parameter estimates

Abstract

For the study of Ising models of general spin S on the square lattice, we have combined our recently extended high-temperature expansions with the low-temperature expansions derived some time ago by Enting, Guttmann and Jensen. We have computed for the first time various critical parameters and improved the estimates of others. Moreover the properties of hyperscaling and of universality (spin S independence) of exponents and of various dimensionless amplitude combinations have been verified accurately. Assuming the validity of the lattice-lattice scaling, from our estimates of critical amplitudes for the square lattice we have also obtained estimates of the corresponding amplitudes for the spin S Ising model on the triangular, honeycomb, and kagome` lattices.