Glass models on Bethe lattices

TL;DR

This paper analyzes lattice glass models on Bethe lattices using the cavity method, exploring phase diagrams, glassy phases, and kinetic effects that influence glass transitions.

Contribution

It introduces a detailed analysis of phase behavior and glassy states in lattice glass models on Bethe lattices, including the impact of dynamics on glass transition.

Findings

Identification of phase diagram with vitreous phase

Analysis of configurational entropy and energy landscape

Kinetic freezing can prevent equilibrium glass transitions

Abstract

We consider ``lattice glass models'' in which each site can be occupied by at most one particle, and any particle may have at most l occupied nearest neighbors. Using the cavity method for locally tree-like lattices, we derive the phase diagram, with a particular focus on the vitreous phase and the highest packing limit. We also study the energy landscape via the configurational entropy, and discuss different equilibrium glassy phases. Finally, we show that a kinetic freezing, depending on the particular dynamical rules chosen for the model, can prevent the equilibrium glass transitions.