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

Abstract

The spherical mean field approximation of a spin-1 model with p-body quenched disordered interaction is investigated. 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 different nature. In 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 are 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.PACS numbers: 64.70.Q-,05.70.Fh,75.10.Nr Random, thermodynamic and inverse first order transitions

Dynamical arrest with zero complexity: The unusual behavior of the spherical Blume-Emery-Griffiths disordered model

“…This is at difference with respect to the static results of Ref. [13], where the high density phase is supposed to be still paramagnetic for T = 0.34.…”

“…Up to the prevuoius case, our dynamic analysis confirms the results of the static one [13]. However, as we anticipated in section I, for D > D th , our dynamical equation yield dynamic arrest at finite temperature when starting from the PM + phase, an effect that was not identified in the static analysis, where the thermodynamically dominant phase is low density PM − .…”

“…The solution with the intermediate value of d turns out to be always unstable (see Ref. [13]), leaving only a high-density and a low-density solutions. Since the density d has a continuous behavior along the PM−/SG thermodynamic transition, Eq.…”

“…Here we will just comment on them briefly to adequately introduce our dynamical study, along with statics novelties with respect to previous analysis. The interested reader can find all the details in [13].…”

“…We computed both quantities using replica theory as in Ref. [13] and report the corresponding curves in figures 5 and 6. We see that the usual RFOT picture does not hold for all values of D along the new dynamical arrest line.…”