The Falicov-Kimball model is a lattice model of itinerant spinless fermions
("electrons") interacting by an on-site potential with classical particles
("ions"). We continue the investigations of the crystalline ground states that
appear for various filling of electrons and ions, 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 is studied. The flux phase problem where one has to find the
optimal flux configurations and the nuclei configurations is also solved in
some cases. Finaly we consider a model where the fermions are replaced by
hard-core bosons. This model also has crystalline ground states. Therefore
their existence does not require the Pauli principle, but only the on-site
hard-core constraint for the itinerant particles.Comment: 42 pages, uuencoded postscript file. Missing pages adde
