Activity phase transition for constrained dynamics

TL;DR

This paper investigates finite size effects and phase coexistence in kinetically constrained models, specifically East and FA-1f, focusing on activity fluctuations and phase transitions in different dimensions.

Contribution

It analyzes finite size effects and phase coexistence in constrained dynamics models, extending understanding of activity phase transitions to higher dimensions and various boundary conditions.

Findings

Finite size effects depend on dimension and boundary conditions.

Phase coexistence occurs between active and inactive phases.

Finite size effects influence the nature of the phase transition.

Abstract

We consider two cases of kinetically constrained models, namely East and FA-1f models. The object of interest of our work is the activity A(t) defined as the total number of configuration changes in the interval [0,t] for the dynamics on a finite domain. It has been shown in [GJLPDW1,GJLPDW2] that the large deviations of the activity exhibit a non-equilibirum phase transition in the thermodynamic limit and that reducing the activity is more likely than increasing it due to a blocking mechanism induced by the constraints. In this paper, we study the finite size effects around this first order phase transition and analyze the phase coexistence between the active and inactive dynamical phases in dimension 1. In higher dimensions, we show that the finite size effects are also determined by the dimension and the choice of boundary conditions.