  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.
