LONG-RANGE ORDER IN A SIMPLE-MODEL OF INTERACTING FERMIONS

We consider a model of spinless fermions on a lattice, interacting through a nearest neighbor repulsion. In the half-filled band case and for dimensions d greater-than-or-equal-to 2, we rigorously prove that there is long-range order in some domain of the parameters beta = (k(B)T)-1 and t/U, where t is the hopping amplitude of the particles, U the strength of their repulsion, and beta the inverse temperature. Our technique is based on the usual Peierls argument of classical statistical mechanics but fails for the groundstate. We discuss the specific difficulties introduced by the Fermi statistics.