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In this paper, we study the Hubbard model with intersite Coulomb interactionin the ionic limit (i.e. no kinetic energy). It is shown that this model isisomorphic to the spin-1 Ising model in presence of a crystal field and anexternal magnetic field. We show that for such models it is possible to find,for any dimension, a finite complete set of eigenoperators and eigenvalues ofthe Hamiltonian. Then, the hierarchy of the equations of motion closes andanalytical expressions for the relevant Green's functions and correlationfunctions can be obtained. These expressions are formal because these functionsdepend on a finite set of unknown parameters, and only a set of exact relationsamong the correlation functions can be derived. In the one-dimensional case weshow that by means of algebraic constraints it is possible to obtain extraequations which close the set and allow us to obtain a complete exact solutionof the model. The behavior of the relevant physical properties for the 1Dsystem is reported.Comment: 19 pages, 9 figures, 16 panel

The extended Hubbard model in the ionic limit