Gi. Watson et R. Lemanski, THE GROUND-STATE PHASE-DIAGRAM OF THE 2-DIMENSIONAL FALICOV-KIMBALL MODEL, Journal of physics. Condensed matter, 7(49), 1995, pp. 9521-9542
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.