  We study the influence of an external magnetic field h on the phase diagram
of a system of Fermi particles living on the sites of a Bethe lattice with
coordination number z and interacting through on-site U and nearest-neighbor V
interactions. This is a physical realization of the extended Hubbard model in
the narrow-band limit. Our results establish that the magnetic field may
dramatically affect the critical temperature below which a long-range charge
ordered phase is observed, as well as the behavior of physical quantities,
inducing, for instance, magnetization plateaus in the magnetization curves.
Relevant thermodynamic quantities - such as the specific heat and the
susceptibility - are also investigated at finite temperature by varying the
on-site potential, the particle density and the magnetic field.
