  We study the phase diagram at finite temperature of a system of Fermi
particles on the sites of the Bethe lattice with coordination number z and
interacting through onsite U and nearest-neighbor V interactions. This is a
physical realization of the extended Hubbard model in the atomic limit. By
using the equations of motion method, we exactly solve the model. For an
attractive intersite potential, we find, at half filling, a phase transition
towards a broken particle-hole symmetry state. The critical temperature, as a
function of the relevant parameters, has a re-entrant behavior as already
observed in the equivalent spin-1 Ising model on the Bethe lattice.
