Random, thermodynamic and inverse first-order transitions in the Blume-Capel spin glass

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