GROUND-STATE CONFIGURATIONS OF THE ONE-DIMENSIONAL FALICOV-KIMBALL MODEL

We consider the one-dimensional Falicov-Kimball lattice model as well as a continuum model, where the attractive potential between the elect rons and the nuclei is a 8 function, with an equal number N of classic al ''nuclei'' and fermion ''electrons.'' We find the exact leading beh avior of the ground-state energy as a function of U for U > U(c). The error term is rigorously estimated. For fixed N the system forms ''ato ms'' which have an effective repulsion between them. From this we argu e that when N becomes infinite the ground-state configurations of the nuclei should be periodic. The low-temperature structure of the model is also discussed.