  We calculate the restricted phase diagram for the Falicov-Kimball model on a
two-dimensional square lattice. We consider the limit where the conduction
electron density is equal to the localized electron density, which is the limit
related to the S_z=0 states of the Hubbard model. After considering over 20,000
different candidate phases (with a unit cell of 16 sites or less) and their
thermodynamic mixtures, we find only about 100 stable phases in the
ground-state phase diagram. We analyze these phases to describe where stripe
phases occur and relate these discoveries to the physics behind stripe
formation in the Hubbard model.
