Condensation in models with factorized and pair-factorized stationary states

TL;DR

This paper reviews models of non-equilibrium condensation with factorized stationary states and introduces a new misanthrope process with parallel dynamics that exhibits condensation with a pair-factorized stationary state.

Contribution

It provides a comprehensive review of existing models and introduces a novel misanthrope process with parallel updates that demonstrates condensation with a pair-factorized stationary state.

Findings

Zero-range and misanthrope processes can exhibit condensation.

A new misanthrope process with parallel dynamics also shows condensation.

The stationary states can be factorized or pair-factorized depending on the model.

Abstract

Non-equilibrium real-space condensation is a phenomenon in which a finite fraction of some conserved quantity (mass, particles, etc.) becomes spatially localised. We review two popular stochastic models of hopping particles that lead to condensation and whose stationary states assume a factorized form: the zero-range process and the misanthrope process, and their various modifications. We also introduce a new model - a misanthrope process with parallel dynamics - that exhibits condensation and has a pair-factorized stationary state.