Spatial Particle Condensation for an Exclusion Process on a Ring

TL;DR

This paper analyzes a simple exclusion process on a ring, providing exact calculations that challenge previous claims of a phase transition, and suggests no such transition exists in the model.

Contribution

It offers the first exact analysis of the stationary state of the model, disputing earlier phase transition claims and clarifying the nature of spatial condensation.

Findings

No phase transition in the grand canonical ensemble.

Fluctuation analysis supports absence of phase transition.

Exact calculations clarify the model's stationary state.

Abstract

We study the stationary state of a simple exclusion process on a ring which was recently introduced by Arndt {\it et al} [J. Phys. A {\bf 31} (1998) L45;cond-mat/9809123]. This model exhibits spatial condensation of particles. It has been argued that the model has a phase transition from a ``mixed phase'' to a ``disordered phase''. However, in this paper exact calculations are presented which, we believe, show that in the framework of a grand canonical ensemble there is no such phase transition. An analysis of the fluctuations in the particle density strongly suggests that the same result also holds for the canonical ensemble.