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

TL;DR

This paper investigates the complex dynamics of a spherical mean-field spin model exhibiting glass transitions, revealing novel regimes including inverted transition lines and a new dynamical arrest phenomenon.

Contribution

It introduces a detailed analysis of the spherical Blume-Emery-Griffiths model, uncovering unique dynamic and thermodynamic transition scenarios, including an inversion of static and dynamic transition lines.

Findings

Identification of regimes with inverted static and dynamic transition lines.

Discovery of a new dynamical arrest line at higher temperature.

Analysis of phase coexistence and transition types in the model.

Abstract

The short- and long-time dynamics of model systems undergoing a glass transition with apparent inversion of Kauzmann and dynamical arrest glass transition lines is investigated. These models belong to the class of the spherical mean-field approximation of a spin-$1$ model with $p$-body quenched disordered interaction, with $p>2$, termed spherical Blume-Emery-Griffiths models. 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 specific regions of the phase diagram coexistence of low density and high density paramagnets can occur, as well as the coexistence of spin-glass and paramagnetic phases. The exact static solution for the glassy phase is known to be 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) for mean-field glasses preceded by a dynamic transition, (ii) a thermodynamic first-order transition with phase coexistence and latent heat and (iii) a regime of apparent inversion of static transition line and dynamic transition lines, the latter defined as a non-zero complexity line. The latter inversion, though, turns out to be preceded by a novel dynamical arrest line at higher temperature. Crossover between different regimes is analyzed by solving mode coupling theory equations throughout the space of external thermodynamic parameters and the relationship with the underlying statics is discussed.