Random, thermodynamic and inverse first-order transitions in the Blume–Capel spinglass

Abstract

A class of model systems undergoing a glass transition with inversion of the fluid and glassyphase in temperature is investigated in order to qualitatively characterize the so-calledinverse freezing phenomenon occurring in some complex glassy polymeric systems such asmethylcellulose. The leading model we analyze is the spherical mean-field approximation of a spin-1 modelwith p-body quenched disordered interaction. Depending on temperature and chemical potentialthe system is found in a paramagnetic or in a glassy phase and the transition between thesephases can be of a different nature. In the given conditions inverse freezing occurs. Asp = 2 theglassy phase is replica-symmetric and the transition is always continuous in the phase diagram. Forp > 2 the exact solution for the glassy phase is obtained by the one-step replica symmetrybreaking ansatz. Different scenarios arise for both the dynamic and the thermodynamictransitions. These include (i) the usual random first-order transition (Kauzmann-like)preceded by a dynamic transition, typical of mean-field glasses, (ii) a thermodynamicfirst-order transition with phase coexistence and latent heat and (iii) a regime of inversionof static and dynamic transition lines. In the latter case a thermodynamic stable glassyphase, with zero configurational entropy, is dynamically accessible from the paramagneticphase. Crossover between different transition regimes is analyzed by means of replicasymmetry breaking theory and a detailed study of the complexity and of the stability ofthe static solution is performed throughout the space of external thermodynamicparameters.