Thermodynamic Properties and Phase Transitions in a Mean-Field Ising Spin Glass on Lattice Gas: the Random Blume-Emery-Griffiths-Capel Model

TL;DR

This paper analyzes the thermodynamic behavior and phase transitions of a mean-field Ising spin glass model with lattice gas characteristics, revealing both continuous and discontinuous transitions with detailed solutions at zero temperature.

Contribution

It provides a comprehensive mean-field analysis of the Random Blume-Emery-Griffiths-Capel model, including phase transition types and solutions using the full replica symmetry breaking scheme.

Findings

Identifies second-order and first-order phase transitions.

Solves Parisi equations down to zero temperature.

Describes coexistence of phases at first-order transition.

Abstract

The study of the mean-field static solution of the Random Blume-Emery-Griffiths-Capel model, an Ising-spin lattice gas with quenched random magnetic interaction, is performed. The model exhibits a paramagnetic phase, described by a stable Replica Symmetric solution. When the temperature is decreased or the density increases, the system undergoes a phase transition to a Full Replica Symmetry Breaking spin-glass phase. The nature of the transition can be either of the second order (like in the Sherrington-Kirkpatrick model) or, at temperature below a given critical value, of the first order in the Ehrenfest sense, with a discontinuous jump of the order parameter and accompanied by a latent heat. In this last case coexistence of phases takes place. The thermodynamics is worked out in the Full Replica Symmetry Breaking scheme, and the relative Parisi equations are solved using a pseudo-spectral method down to zero temperature.