Multiple time scales from hard local constraints: glassiness without disorder

TL;DR

This paper demonstrates that multiple time scales can emerge in systems without disorder due to local constraints, with dynamics governed by a growing length scale and a hierarchy of fast and slow regions, offering insights into glassy behavior.

Contribution

It introduces a simple model showing multiple time scales and hierarchical dynamics arising solely from local constraints, without disorder, providing a new perspective on glassiness.

Findings

Multiple time scales emerge without disorder.

Hierarchy of fast and slow regions in real space.

Slowing down linked to growth of mobile excitations.

Abstract

While multiple time scales generally arise in the dynamics of disordered systems, we find multiple time scales in absence of disorder, in a simple model with hard local constraints. The dynamics of the model, which consists of local collective rearrangements of various scales, is not determined by the smallest scale but by a length $l^*$ that grows at low energies. In real space we find a hierarchy of fast and slow regions: each slow region is geometrically insulated from all faster degrees of freedom, which are localized in fast pockets below percolation thresholds. A tentative analogy with structural glasses is given, which attributes the slowing down of the dynamics to the growing size of mobile elementary excitations, rather than to the size of some domains.