The free energy in a magnetic field and the universal scaling equation of state for the three-dimensional Ising model

TL;DR

This paper extends high-temperature and low-magnetic-field expansions of the free energy for the 3D Ising model and related systems, enabling more precise tests of universality and scaling near criticality.

Contribution

It provides extended bivariate expansions for the free energy and susceptibilities for various spin systems and lattice structures within the 3D Ising universality class.

Findings

More accurate critical scaling and universality tests.

Improved parametric representation of the critical equation of state.

Extended high-temperature expansions up to K^24.

Abstract

We have substantially extended the high-temperature and low-magnetic-field (and the related low-temperature and high-magnetic-field) bivariate expansions of the free energy for the conventional three-dimensional Ising model and for a variety of other spin systems generally assumed to belong to the same critical universality class. In particular, we have also derived the analogous expansions for the Ising models with spin s=1,3/2,.. and for the lattice euclidean scalar field theory with quartic self-interaction, on the simple cubic and the body-centered cubic lattices. Our bivariate high-temperature expansions, which extend through K^24, enable us to compute, through the same order, all higher derivatives of the free energy with respect to the field, namely all higher susceptibilities. These data make more accurate checks possible, in critical conditions, both of the scaling and the universality properties with respect to the lattice and the interaction structure and also help to improve an approximate parametric representation of the critical equation of state for the three-dimensional Ising model universality class.