LONG-RANGE ORDER IN THE FALICOV-KIMBALL MODEL - EXTENSION OF KENNEDY-LIEB THEOREM

We study the Falicov-Kimball model on Z(d), d greater-than-or-equal-to 2, in the grand canonical ensemble with chemical potentials mu(e) for the itinerant fermions (''electrons'') and mu(n) for the static parti cles (''nuclei''). There is an on site attraction -2U between electron s and nuclei. Kennedy and Lieb showed that, at the symmetry point mu(e ) = mu(n) = -U, at which, for all temperatures the average densities o f both electrons and nuclei equal to 1/2, this model exhibits crystall ine order for sufficiently low temperatures with the nuclei (and elect rons) occupying predominantly the even or odd sublattices. In this pap er we extend the results of Kennedy and Lieb to a strip in the (mu(e), mu(n)) plane, surrounding the symmetry point, whenever U and beta/U a re large (beta is the inverse temperature). This means we need not hav e equal densities of electrons and nuclei as long as they are both clo se to 1/2.