Emergent facilitation by random constraints in a facilitated random walk model of glass

TL;DR

This paper introduces a lattice model called facilitated random walk (FRW) that captures glassy dynamics through kinetic constraints and dynamic interactions, reproducing key features like relaxation and heterogeneity without explicit facilitation rules.

Contribution

The paper presents the FRW model, a novel kinetically constrained lattice model that exhibits glass-like behavior through reversible dynamic interactions, bridging defect and atomistic models.

Findings

FRW exhibits stretched exponential relaxation.

The model shows dynamical heterogeneity similar to glasses.

Facilitation behaviors emerge without explicit facilitation rules.

Abstract

The physics of glass has been a significant topic of interest for decades. Dynamical facilitation is widely believed to be an important characteristic of glassy dynamics, but the precise mechanism is still under debate. We propose a lattice model of glass called the facilitated random walk (FRW). Each particle performs continuous time random walk in the presence of its own random local kinetic constraints. The particles do not interact energetically. Instead, they interact kinetically with a hopping rate resampling rule under which motions of a particle can randomly perturb the local kinetic constraints of other particles. This dynamic interaction is reversible, following a rate restoration rule. A step-by-step reversal of the particle motions exactly restore the previous constraints, modeling randomness quenched in the configuration space of glass. The model exhibits stretched exponential relaxation and dynamical heterogeneity typical of glasses. Despite the lack of explicit facilitation rule, the FRW shows facilitation behaviors closely analogous to those of the kinetically constrained models (KCM). The FRW is a coarse-grained version of the distinguishable particle lattice model (DPLM) and this exemplifies that compatible defect and atomistic models can complement each other on the study of glass.