Charge orderings in the atomic limit of the extended Hubbard model

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 $\frac{1}{2}U$, exchange interaction W in an effective magnetic field ${\left( \mu - \frac{1}{2}U - z_{0}W\right) }$. 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