Anomalous nucleation far from equilibrium

TL;DR

This paper investigates the nucleation process in an asymmetric exclusion system far from equilibrium, revealing complex finite size effects and proposing a scenario that explains the apparent discrepancy between earlier simulations and analytic conjectures.

Contribution

It introduces a detailed analysis of finite size effects in a two-species driven lattice model, proposing a nucleation scenario that reconciles conflicting previous findings.

Findings

Presence of a single macroscopic cluster as an intermediate nucleation stage

Different cluster size distributions in small and large systems

Exponential cluster size distributions governed by distinct length scales

Abstract

We present precision Monte Carlo data and analytic arguments for an asymmetric exclusion process, involving two species of particles driven in opposite directions on a $2 \times L$ lattice. We propose a scenario which resolves a stark discrepancy between earlier simulation data, suggesting the existence of an ordered phase, and an analytic conjecture according to which the system should revert to a disordered state in the thermodynamic limit. By analyzing the finite size effects in detail, we argue that the presence of a single, seemingly macroscopic, cluster is an intermediate stage of a complex nucleation process: In smaller systems, this cluster is destabilized while larger systems allow the formation of multiple clusters. Both limits lead to exponential cluster size distributions which are, however, controlled by very different length scales.