Phase separation in disordered exclusion models

TL;DR

This paper reviews how quenched disorder causes phase separation in one-dimensional asymmetric exclusion processes, providing exact critical densities for particlewise disorder and bounds for sitewise disorder, along with domain coarsening analysis.

Contribution

It offers a comprehensive review of disorder-induced phase separation in exclusion models, including exact calculations and scaling analysis, connecting to directed polymer results.

Findings

Particlewise disorder allows exact critical density calculation.

Sitewise disorder only yields bounds on critical density.

Domain coarsening analyzed using scaling and extremal statistics.

Abstract

The effect of quenched disorder in the one-dimensional asymmetric exclusion process is reviewed. Both particlewise and sitewise disorder generically induces phase separation in a range of densities. In the particlewise case the existence of stationary product measures in the homogeneous phase implies that the critical density can be computed exactly, while for sitewise disorder only bounds are available. The coarsening of phase-separated domains starting from a homogeneous initial condition is addressed using scaling arguments and extremal statistics considerations. Some of these results have been obtained previously in the context of directed polymers subject to columnar disorder.