  The spinless Falicov-Kimball model is solved exactly in the limit of
infinite-dimensions on both the hypercubic and Bethe lattices. The competition
between segregation, which is present for large U, and charge-density-wave
order, which is prevalent at moderate U, is examined in detail. We find a rich
phase diagram which displays both of these phases. The model also shows
nonanalytic behavior in the charge-density-wave transition temperature when U
is large enough to generate a correlation-induced gap in the single-particle
density of states.
