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We study the one- and two- dimensional extended Hubbard model by means of theComposite Operator Method within the 2-pole approximation. The fermionicpropagator 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 sourcesof information regarding the instability of the paramagnetic (metal andinsulator) phase towards charge ordering driven by the intersite Coulombinteraction. Very rich phase diagrams (multiple first and second order phasetransitions, critical points, reentrant behavior) have been found and discussedwith respect to both metal-insulator and charge ordering transitions: theconnections with the experimental findings relative to some manganese compoundsare analyzed. Moreover, the possibility of improving the capability ofdescribing cuprates with respect to the simple Hubbard model is discussedthrough the analysis of the Fermi surface and density of states features. Wealso report about the specific heat behavior in presence of the intersiteinteraction and the appearance of crossing points.Comment: 15 pages, 36 figure

The Hubbard model with intersite interaction within the Composite Operator Method