Segregation and charge-density-wave order in the spinless Falicov-Kimball model

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 that 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.