  We show that a system of spinless Fermi particles, localized on the sites of
the Bethe lattice with coordination number z and interacting through a
repulsive nearest-neighbor interaction, exhibits a phase transition to a
charge-ordered state. The phase diagram in the n-T plane is derived. Relevant
thermodynamic quantities, such as the free energy, the specific heat, the
entropy and the compressibility are analyzed in detail.
