Condensation in stochastic lattice gases with size-dependent stationary weights

TL;DR

This paper studies phase separation in stochastic lattice gases with size-dependent weights, identifying conditions for condensation and characterizing cluster size distributions through theoretical analysis and simulations.

Contribution

It introduces a novel derivation of cluster size distribution using size-biased sampling, extending previous models to systems with size-dependent weights.

Findings

Condensation occurs when particle density exceeds a critical value.

The cluster size distribution is derived using size-biased sampling.

Simulations confirm theoretical predictions on condensate size and distribution.

Abstract

We consider stochastic lattice gases with stationary product weights and a polynomial perturbation vanishing with the system size that leads to condensation. If the density of particles exceeds a critical value the system phase separates into a bulk with homogeneous distribution of particles and a condensed phase. Depending on parameter values, the latter consists of a single macroscopic cluster or a diverging number of independent clusters on a smaller scale. We establish the condensation transition via the equivalence of ensembles and the main novelty is a derivation of the cluster size distribution using size-biased sampling, generalizing previous work on zero-range and inclusion processes. Simulations of zero-range processes illustrate our theoretical results on the condensate scale and size distribution.