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

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.