  In this paper the two dimensional extended Hubbard model with intersite
magnetic Ising-like interaction in the atomic limit is analyzed by means of the
classical Monte Carlo method in the grand canonical ensemble. Such an effective
simple model could describe behavior of insulating (anti)ferromagnets. In the
model considered the Coulomb interaction ($U$) is on-site and the magnetic
interactions in $z$-direction ($J>0$, antiferromagnetic) are restricted to
nearest-neighbors. Simulations of the model have been performed on a square
lattice consisting of $N=L\times L=400$ sites ($L=20$) in order to obtain the
full phase diagram for $U/(4J)=1$. Results obtained for on-site repulsion
($U>0$) show that, apart from homogeneous non-ordered (NO) and ordered magnetic
(antiferromagnetic, AF) phases, there is also a region of phase separation (PS:
AF/NO) occurrence. We present a phase diagram as well as some thermodynamic
properties of the model for the case of $U/(4J)=1$ (and arbitrary chemical
potential and arbitrary electron concentration). The AF-NO transition can be
second-order as well as first-order and the tricritical point occurs on the
diagram.
