Finite size effects and metastability in zero-range condensation

TL;DR

This paper investigates finite size effects and metastability in zero-range processes exhibiting condensation, revealing significant deviations from thermodynamic limit predictions near criticality, with implications for practical systems like traffic and granular flow.

Contribution

It provides a rigorous analysis of finite size effects and metastable phases in zero-range condensation, highlighting the failure of the thermodynamic limit to capture key dynamics.

Findings

Finite size effects cause metastability near critical density.

Discontinuity in system behaviour is established at a scaling limit.

Metastable phases are characterized by current matching and fluid phase extension.

Abstract

We study zero-range processes which are known to exhibit a condensation transition, where above a critical density a non-zero fraction of all particles accumulates on a single lattice site. This phenomenon has been a subject of recent research interest and is well understood in the thermodynamic limit. The system shows large finite size effects, and we observe a switching between metastable fluid and condensed phases close to the critical point, in contrast to the continuous limiting behaviour of relevant observables. We describe the leading order finite size effects and establish a discontinuity near criticality in a rigorous scaling limit. We also characterise the metastable phases using a current matching argument and an extension of the fluid phase to supercritical densities. This constitutes an interesting example where the thermodynamic limit fails to capture essential parts of the dynamics, which are particularly relevant in applications with moderate system sizes such as traffic flow or granular clustering.