Free Energy and Equation of State of Ising-like Magnet Near the Critical Point

TL;DR

This paper develops a collective variables method to analyze the free energy, equation of state, and susceptibility of a 3D Ising-like magnet near its critical point, providing results consistent with existing theories and simulations.

Contribution

It introduces a parametrization-free, microscopic approach using renormalization group transformations to study critical phenomena in Ising-like systems.

Findings

Derived expressions for free energy, equation of state, and susceptibility.

Calculated critical exponents for correlation length and order parameter.

Results qualitatively agree with Monte Carlo simulations and parametric models.

Abstract

The description of a three-dimensional Ising-like magnet in the presence of an external field in the vicinity of the critical point by the collective variables method is proposed. Using the renormalization group transformations, the scaling region size is defined as a function of temperature and field. The obtained expressions for the free energy, equation of state and susceptibility allow one to analyse their dependence on microscopic parameters of the system. The critical exponents of the correlation length and order parameter are calculated as well. The results agree qualitatively with ones obtained within the framework of the parametric representation of the equation of state and Monte-Carlo simulations. The calculations do not involve any parametrization, phenomenological assumptions and adjustable parameters. The approach can be extended to models with a multicomponent order parameter.