  The observation of charge stripe order in the doped nickelate and cuprate
materials has motivated much theoretical effort to understand the underlying
mechanism of the stripe phase. Numerical studies of the Hubbard model show two
possibilities: (i) stripe order arises from a tendency toward phase separation
and its competition with the long-range Coulomb interaction or (ii) stripe
order inherently arises as a compromise between itinerancy and magnetic
interactions. Here we determine the restricted phase diagrams of the
two-dimensional Falicov-Kimball model and see that it displays rich behavior
illustrating both possibilities in different regions of the phase diagram.
