Phase transitions in the three-state Ising spin-glass model with finite connectivity

TL;DR

This paper extends the statistical mechanics analysis of finite connectivity spin glasses to a three-state model, revealing complex phase transitions including reentrant behavior and inverse freezing phenomena.

Contribution

It introduces a replica method for the three-state Ghatak-Sherrington model with finite connectivity, providing detailed phase diagrams and transition characteristics.

Findings

Reentrant phase boundaries observed

Presence of both continuous and first-order transitions

Identification of inverse freezing behavior

Abstract

The statistical mechanics of a two-state Ising spin-glass model with finite random connectivity, in which each site is connected to a finite number of other sites, is extended in this work within the replica technique to study the phase transitions in the three-state Ghatak-Sherrington (or random Blume-Capel) model of a spin glass with a crystal field term. The replica symmetry ansatz for the order function is expressed in terms of a two-dimensional effective-field distribution which is determined numerically by means of a population dynamics procedure. Phase diagrams are obtained exhibiting phase boundaries which have a reentrance with both a continuous and a genuine first-order transition with a discontinuity in the entropy. This may be seen as "inverse freezing", which has been studied extensively lately, as a process either with or without exchange of latent heat.