On the dynamics of the glass transition on Bethe lattices

TL;DR

This paper investigates the slow dynamics and glass transition in disordered spin models on Bethe lattices, focusing on large scale rearrangements and a zero-temperature tricritical point, with broader implications for similar systems.

Contribution

It provides a detailed analysis of the dynamical glass transition on Bethe lattices, emphasizing large scale rearrangements and the role of a zero-temperature tricritical point, extending the understanding of glassy dynamics.

Findings

Identification of large scale rearrangements controlling slow dynamics

Characterization of the dynamical glass transition near the tricritical point

Conjecture of broader applicability of the results

Abstract

The Glauber dynamics of disordered spin models with multi-spin interactions on sparse random graphs (Bethe lattices) is investigated. Such models undergo a dynamical glass transition upon decreasing the temperature or increasing the degree of constrainedness. Our analysis is based upon a detailed study of large scale rearrangements which control the slow dynamics of the system close to the dynamical transition. Particular attention is devoted to the neighborhood of a zero temperature tricritical point. Both the approach and several key results are conjectured to be valid in a considerably more general context.