We study a simple effective model for description of charge orderings in narrow band materials, i.e. the spinless fermion model with repulsive intersite interaction W . The analysis is concentrated on the problem of phase separations and the effects of next-nearest neighbor hopping t2 on the charge ordered states in this system. The cases of d-dimensional (d ≥ 2) hypercubic lattices are considered for arbitrary particle concentration (0 < n < 1). Within the broken symmetry Hartree-Fock approximation the phase diagrams as a function of W and n are evaluated for representative cases. The results for t 2 = 0 are compared with those found for the case with nearest neighbor hopping only.

The model of local electron pairs and itinerant fermions coupled via charge exchange mechanism, which mutually induces superconductivity in both subsystems is studied for anisotropic pairing symmetry. The phase diagram is presented and the phase fluctuations effects are analyzed within the Kosterlitz-Thouless scenario.

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