Thermodynamics of the Fredrickson-Andersen Model on the Bethe Lattice

TL;DR

This paper analytically studies the static properties of the Fredrickson-Andersen model on the Bethe lattice, revealing an ergodicity-breaking transition and providing insights into glassy dynamics and correlations.

Contribution

It presents an exact solution for the statics of the FAM on the Bethe lattice, including new cavity equations and analysis of the ergodicity-breaking transition.

Findings

Identification of a glassy phase with blocked spins

Analytical computation of self-overlap and configurational entropy

Development of algorithms for fast equilibration and dynamics

Abstract

The statics of the Fredrickson-Andersen model (FAM) of the liquid-glass transition is solved on the Bethe lattice (BL). The kinetic constraints of the FAM imply on the BL an ergodicity-breaking transition to a (glassy) phase where a fraction of spins of the system is permanently blocked, and the remaining "free" spins become non-trivially correlated. We compute several observables of the ergodicity-broken phase, such as the self-overlap, the configurational entropy and the spin-glass susceptibility, and we compare the analytical predictions with numerical experiments. The cavity equations that we obtain allow to define algorithms for fast equilibration and accelerated dynamics. We find that at variance with spin-glass models, the correlations inside a state do not exhibit a critical behavior.