Stable Solution of the Simplest Spin Model for Inverse Freezing

TL;DR

This paper provides a thorough analysis of the Blume-Emery-Griffiths spin model with disorder, revealing stable inverse freezing behavior and comparing it with related models, including the Ghatak-Sherrington model, across the phase diagram.

Contribution

It introduces a stable thermodynamic solution for the simplest spin model exhibiting inverse freezing, using Full Replica Symmetry Breaking.

Findings

The model exhibits inverse freezing with stable phases.

Comparison shows differences in reentrance behavior among related models.

The Ghatak-Sherrington model captures key features of inverse transitions.

Abstract

We analyze the Blume-Emery-Griffiths model with disordered magnetic interaction that displays the inverse freezing phenomenon. The behavior of this spin-1 model in crystal field is studied throughout the phase diagram and the transition and spinodal lines for the model are computed using the Full Replica Symmetry Breaking Ansatz that always yields a thermodynamically stable phase. We compare the results both with the formulation of the same model in terms of Ising spins on lattice gas, where no reentrance takes place, and with the model with generalized spin variables recently introduced by Schupper and Shnerb [Phys. Rev. Lett. {\bf 93} 037202 (2004)], for which the reentrance is enhanced as the ratio between the degeneracy of full to empty sites increases. The simplest version of all these models, known as the Ghatak-Sherrington model, turns out to hold all the general features characterizing an inverse transition to an amorphous phase, including the right thermodynamic behavior.