THE GROUND-STATE PHASE-DIAGRAM OF THE 2-DIMENSIONAL FALICOV-KIMBALL MODEL

The spinless Falicov-Kimball model on a two-dimensional square lattice is studied using the method of restricted phase diagrams constructed in the grand canonical ensemble. The results are compared with the one -dimensional model. Although the two-dimensional phase diagrams are mo re complex, with several distinct families of ion configurations occur ring as ground states, there are surprising similarities with the one- dimensional case. Within each family of configurations, the ground sta tes form a devil's staircase structure and the configurations are cons tructed according to a composition rule identical to that in one dimen sion. It is also found that, as in one dimension, segregation occurs i n the non-neutral model for large ion-electron interaction strength. S ome features of the phase diagrams are understood by examining the eff ective two-body ion interaction.