From Large Scale Rearrangements to Mode Coupling Phenomenology

TL;DR

This paper analyzes the equilibrium dynamics of Ising spin models with multi-spin interactions on sparse random graphs, identifying large-scale rearrangements that explain the slowing down near the glass transition.

Contribution

It provides an exact characterization of the dynamics near criticality by analyzing the statistical properties of large-scale rearrangements in these models.

Findings

Identified large-scale rearrangements responsible for dynamical slowing-down.

Characterized the dynamics near the glass transition exactly.

Applicable to various glassy models on sparse random graphs.

Abstract

We consider the equilibrium dynamics of Ising spin models with multi-spin interactions on sparse random graphs (Bethe lattices). Such models undergo a mean field glass transition upon increasing the graph connectivity or lowering the temperature. Focusing on the low temperature limit, we identify the large scale rearrangements responsible for the dynamical slowing-down near the transition. We are able to characterize exactly the dynamics near criticality by analyzing the statistical properties of such rearrangements. Our approach can be generalized to a large variety of glassy models on sparse random graphs, ranging from satisfiability to kinetically constrained models.