  We study the one- and two- dimensional extended Hubbard model by means of the
Composite Operator Method within the 2-pole approximation. The fermionic
propagator is computed fully self-consistently as a function of temperature,
filling and Coulomb interactions. The behaviors of the chemical potential
(global indicator) and of the double occupancy and nearest-neighbor density-
density correlator (local indicators) are analyzed in detail as primary sources
of information regarding the instability of the paramagnetic (metal and
insulator) phase towards charge ordering driven by the intersite Coulomb
interaction. Very rich phase diagrams (multiple first and second order phase
transitions, critical points, reentrant behavior) have been found and discussed
with respect to both metal-insulator and charge ordering transitions: the
connections with the experimental findings relative to some manganese compounds
are analyzed. Moreover, the possibility of improving the capability of
describing cuprates with respect to the simple Hubbard model is discussed
through the analysis of the Fermi surface and density of states features. We
also report about the specific heat behavior in presence of the intersite
interaction and the appearance of crossing points.
