Finite-size effects in dynamics of zero-range processes

TL;DR

This paper investigates finite-size effects in zero-range processes near the condensation transition, revealing how static and dynamic properties change with system size and identifying a finite-size critical density through simulations.

Contribution

It introduces a detailed analysis of finite-size effects in zero-range processes, including the determination of a finite-size critical density and its impact on dynamics.

Findings

Identification of a finite-size critical density { ho}c (L)

Observation of fluid-like behavior above this density

Qualitative change in dynamical properties at { ho}c (L)

Abstract

The finite-size effects prominent in zero-range processes exhibiting a condensation transition are studied by using continuous-time Monte Carlo simulations. We observe that, well above the thermodynamic critical point, both static and dynamic properties display fluid-like behavior up to a density {\rho}c (L), which is the finite-size counterpart of the critical density {\rho}c = {\rho}c (L \rightarrow \infty). We determine this density from the cross-over behavior of the average size of the largest cluster. We then show that several dynamical characteristics undergo a qualitative change at this density. In particular, the size distribution of the largest cluster at the moment of relocation, the persistence properties of the largest cluster and correlations in its motion are studied.