GROUND-STATES AND FLUX CONFIGURATIONS OF THE 2-DIMENSIONAL FALICOV-KIMBALL MODEL

The Falicov-Kimball model is a lattice model of itinerant spinless fer mions (''electrons'') interacting by an on-site potential with classic al particles (''ions''). We continue the investigations of the crystal line ground states that appear for various filling of electrons and io ns for large coupling. We investigate the model for square as well as triangular lattices. New ground states are found and the effects of a magnetic flux on the structure of the phase diagram are studied. The n ux phase problem where one has to find the optimal flux configurations and the nuclei configurations is also solved in some cases. Finally w e consider a model where the fermions are replaced by hardcore: bosons . This model also has crystalline ground states. Therefore their exist ence does not require the Pauli principle, but only the on-site hard-c ore constraint for the itinerant particles.