Phase separation driven by a fluctuating two-dimensional self-affine potential field

TL;DR

This paper investigates how particles in a two-dimensional fluctuating potential landscape driven by KPZ dynamics tend to cluster and phase separate, revealing unique steady-state features and asymmetries not seen in one-dimensional systems.

Contribution

It introduces a study of phase separation driven by a 2D self-affine KPZ landscape, highlighting novel clustering behavior and asymmetries in cluster-size distribution.

Findings

Particles cluster on a growing length scale over time.

The steady state exhibits a cusp in the correlation function.

Cluster-size distribution is asymmetric and includes an infinite cluster.

Abstract

We study phase separation in a system of hard-core particles driven by a fluctuating two-dimensional self-affine potential landscape which evolves through Kardar-Parisi-Zhang (KPZ) dynamics. We find that particles tend to cluster together on a length scale which grows in time. The final phase-separated steady state is characterized by an unusual cusp singularity in the scaled correlation function and a broad distribution for the order parameter. Unlike the one-dimensional case studied earlier, the cluster-size distribution is asymmetric between particles and holes, reflecting the broken reflection symmetery of the KPZ dynamics, and has a contribution from an infinite cluster in addition to a power law part. A study of the surface in terms of coarse-grained depth variables helps understand many of these features.