Space-time thermodynamics and subsystem observables in a kinetically constrained model of glassy systems

TL;DR

This paper explores the analogy between phase coexistence in spacetime and glass transition phenomena, using the one-dimensional FA model to analyze active-inactive phase dynamics and their relation to non-equilibrium universality classes.

Contribution

It develops a detailed analysis of spacetime phase coexistence in the FA model and extends the analogy to non-reversible dynamics within the directed percolation class.

Findings

Evidence of phase coexistence in spacetime observables

Breaking reversibility leads to directed percolation universality

Active-inactive phases relate to glass transition mechanisms

Abstract

In a recent article [M. Merolle et al., Proc. Natl. Acad. Sci. USA 102, 10837 (2005)] it was argued that dynamic heterogeneity in $d$-dimensional glass formers is a manifestation of an order-disorder phenomenon in the $d+1$ dimensions of spacetime. By considering a dynamical analogue of the free energy, evidence was found for phase coexistence between active and inactive regions of spacetime, and it was suggested that this phenomenon underlies the glass transition. Here we develop these ideas further by investigating in detail the one-dimensional Fredrickson-Andersen (FA) model in which the active and inactive phases originate in the reducibility of the dynamics. We illustrate the phase coexistence by considering the distributions of mesoscopic spacetime observables. We show how the analogy with phase coexistence can be strengthened by breaking microscopic reversibility in the FA model, leading to a non-equilibrium theory in the directed percolation universality class.