Multiple time scales from hard local constraints: glassiness without disorder

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.