Glass transition in self organizing cellular patterns

TL;DR

This paper investigates the dynamical behavior of cellular patterns undergoing a phase transition from an equilibrium state to a glassy frozen state, influenced by temperature, using a stochastic Glauber process.

Contribution

It introduces a model for cellular pattern evolution that captures the glass transition and aging phenomena in a non-crystalline system.

Findings

Above critical temperature, patterns reach equilibrium.

Below critical temperature, patterns exhibit glassy freezing.

Persistence function shows exponential decay at high T and aging at low T.

Abstract

We have considered the dynamical evolution of cellular patterns controlled by a stochastic Glauber process determined by the deviations of local cell topology from that of a crystalline structure. Above a critical temperature evolution is towards a common equilibrium state from any initial configuration, but beneath this temperature there is a dynamical phase transition, with a start from a quasi-random state leading to non-equilibrium glassy freezing whereas an ordered start rests almost unchanged. A temporal persistence function decays exponentially in the high temperature equilibrating state but has a characteristic slow non-equilibrium aging-like behaviour in the low temperature glassy phase.