REPULSIVE PARTICLES ON A 2-DIMENSIONAL LATTICE

The problem of finding the minimum-energy configurations of particles on a square lattice, subject to short-ranged repulsive interactions, i s studied analytically. The study is relevant to charge-ordered states of interacting fermions, as described by the spinless Falicov-Kimball model. A simple model is introduced, corresponding to the limit of a two-body potential which is a very rapidly decreasing convex function of distance. Its ground states are found rigorously for certain densit y ranges, including half filling. These agree with known properties of neutral ground states of the large-U Falicov-Kimball model, suggestin g a characterization of the latter as ''most homogeneous'' configurati ons. For lower densities, a family of ground stales is found having th e novel property that they are aperiodic even when the particle densit y is a rational number. In some cases, local phase separation suggests an inherent sensitivity to the detailed form of the interaction poten tial.