Order parameter of a three-dimensional Ising-like system in the simplest and higher non-Gaussian approximations

TL;DR

This paper derives explicit expressions for the order parameter of a three-dimensional Ising-like system using non-Gaussian approximations, revealing how microscopic parameters influence critical behavior.

Contribution

It introduces a method to calculate the order parameter in non-Gaussian approximations for 3D Ising systems, including confluent corrections.

Findings

Order parameter expressions in  and  models

Dependence on temperature and microscopic parameters

Features of successive non-Gaussian approximation calculations

Abstract

The application of the collective variables method to the study of the behaviour of nonuniversal characteristics of the system in the critical region is illustrated by an example of the order parameter. Explicit expressions for the order parameter (the average spin moment) of a three-dimensional uniaxial magnet are obtained in approximations of quartic and sextic non-Gaussian fluctuation distributions (the \rho^4 and \rho^6 models, respectively), taking into account confluent corrections. Some distinctive features appearing in the process of calculating the order parameter on the basis of two successive non-Gaussian approximations are indicated. The dependence of the average spin moment of an Ising-like system on the temperature and microscopic parameters is studied.