Renormalization group study of a kinetically constrained model for strong glasses

TL;DR

This paper develops a dynamic field theory for a kinetically constrained model of strong glasses, analyzing its critical behavior via renormalization group methods and supporting findings with numerical simulations.

Contribution

It introduces a renormalization group analysis of a kinetically constrained model for strong glasses, connecting it to directed percolation universality class.

Findings

Model exhibits a zero-temperature dynamical critical point in d≥2.

Behavior in 1D corresponds to compact directed percolation.

Numerical simulations agree with theoretical predictions.

Abstract

We derive a dynamic field theory for a kinetically constrained model, based on the Fredrickson--Andersen model, which we expect to describe the properties of an Arrhenius (strong) supercooled liquid at the coarse-grained level. We study this field theory using the renormalization group. For mesoscopic length and time scales, and for space dimension d \geq 2, the behaviour of the model is governed by a zero-temperature dynamical critical point in the directed percolation universality class. We argue that in d=1 its behaviour is that of compact directed percolation. We perform detailed numerical simulations of the corresponding Fredrickson-Andersen model on the lattice in various dimensions, and find reasonable quantitative agreement with the field theory predictions.