Subdiffusion and dynamical heterogeneities in a lattice glass model

TL;DR

This paper analyzes a lattice glass model with kinetic constraints and interactions, revealing subdiffusive dynamics and diverging heterogeneity length scales near the critical density, with an exact steady-state solution.

Contribution

It provides an exact solution for the steady-state distribution and characterizes dynamical heterogeneities and subdiffusive behavior in a kinetically constrained lattice glass model.

Findings

Dynamical heterogeneity length scale diverges near critical density

Mobile regions exhibit subdiffusive motion due to self-induced trapping

Exact steady-state distribution can be computed in any dimension

Abstract

We study a kinetically constrained lattice glass model in which continuous local densities are randomly redistributed on neighbouring sites with a kinetic constraint that inhibits the process at high densities, and a random bias accounting for attractive or repulsive interactions. The full steady-state distribution can be computed exactly in any space dimension d. Dynamical heterogeneities are characterized by a length scale that diverges when approaching the critical density. The glassy dynamics of the model can be described as a reaction-diffusion process for the mobile regions. The motion of mobile regions is found to be subdiffusive, for a large range of parameters, due to a self-induced trapping mechanism.