Spin-glass model for inverse freezing

Abstract

We analyze the Blume–Emery–Griffiths model with disordered magnetic interaction displaying the inverse freezing phenomenon. The behaviour of this spin-1 model in crystal fields 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 quenched disordered model with Ising spins on a lattice gas, where no reentrance takes place, and with the model with generalized spin variables recently introduced by Schupper and Shnerb. 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 behaviour.

Notes

†With respect to the classic Clausius–Clapeyron equation D takes the place of the pressure and ρ plays the role of the specific volume.

‡For example, setting S = σn, with n = 0, 1 fast and σ = ±1 slow.