Updated tests of scaling and universality for the spin-spin correlations in the 2D and 3D spin-S Ising models using high-temperature expansions

TL;DR

This paper extends high-temperature series expansions for spin-spin correlations in 2D and 3D spin-S Ising models, confirming the universality and scaling hypotheses through extensive data analysis.

Contribution

It provides the most comprehensive high-temperature series expansions up to order 25 for various lattices, validating key theoretical hypotheses in statistical physics.

Findings

Confirmed the validity of scaling and universality hypotheses

Extended high-temperature series expansions up to order 25

Validated correlation function and correlation-lengths behavior

Abstract

We have extended, from order 12 through order 25, the high-temperature series expansions (in zero magnetic field) for the spin-spin correlations of the spin-S Ising models on the square, simple-cubic and body-centered-cubic lattices. On the basis of this large set of data, we confirm accurately the validity of the scaling and universality hypotheses by resuming several tests which involve the correlation function, its moments and the exponential or the second-moment correlation-lengths.