  The extended Hubbard model in the atomic limit (AL-EHM) on a square lattice
with periodic boundary conditions is studied with use of the Monte Carlo (MC)
method. Within the grand canonical ensemble the phase and order-order
boundaries for charge orderings are obtained. The phase diagrams include three
types of charge ordered phases and the nonordered phase. The system exhibits
very rich structure and shows unusual multicritical behavior. In the limiting
case of tij = 0, the EHM is equivalent to the pseudospin model with single-ion
anisotropy 1/2U, exchange interaction W in an effective magnetic field
(mu-1/2U-zW). This classical spin model is analyzed using the MC method for the
canonical ensemble. The phase diagram is compared with the known results for
the Blume-Capel model.
