Gibbs free energy and Helmholtz free energy for a three-dimensional Ising-like model

TL;DR

This paper analytically derives Gibbs and Helmholtz free energies for a 3D Ising-like model, providing insights into phase stability, metastability, and the microscopic basis of thermodynamic constructions.

Contribution

It introduces a unified analytical approach to compute both free energies and their dependencies in a 3D Ising-like system, including stability analysis.

Findings

Explicit free energy functions as a function of temperature and external field.

Graphical representations of free energy dependencies.

Identification of stability, metastability, and instability regions.

Abstract

The critical behavior of a 3D Ising-like system is studied at the microscopic level of consideration. The free energy of ordering is calculated analytically as an explicit function of temperature, an external field and the initial parameters of the model. Within a unified approach, both Gibbs and Helmholtz free energies are obtained and the dependencies of them on the external field and the order parameter, respectively, are presented graphically. The regions of stability, metastability, and unstability are established on the order parameter-temperature plane. The way of implementation of the well-known Maxwell construction is proposed at microscopic level.