  In this work we focus on the study of phase separation in the zero-bandwidth
extended Hubbard with nearest-neighbors intersite Ising-like magnetic
interactions $J$ and on-site Coulomb interactions $U$. The system has been
analyzed by means of Monte Carlo simulations (in the grand canonical ensemble)
on two dimensional square lattice (with $N=L\times L =400$ sites) and the
results for $U/(4J)=2$ as a function of chemical potential and electron
concentration have been obtained. Depending on the values of interaction
parameters the system exhibits homogeneous (anti-)ferromagnetic (AF) or
non-ordered (NO) phase as well as phase separation PS:AF/NO state. Transitions
between homogeneous phases (i.e. AF-NO transitions) can be of first or second
order and the tricritical point is also present on the phase diagrams. The
electron compressibility $K$ is an indicator of the phase separation and that
quantity is of particular interest of this paper.
