  In this paper, we study the Hubbard model with intersite Coulomb interaction
in the ionic limit (i.e. no kinetic energy). It is shown that this model is
isomorphic to the spin-1 Ising model in presence of a crystal field and an
external magnetic field. We show that for such models it is possible to find,
for any dimension, a finite complete set of eigenoperators and eigenvalues of
the Hamiltonian. Then, the hierarchy of the equations of motion closes and
analytical expressions for the relevant Green's functions and correlation
functions can be obtained. These expressions are formal because these functions
depend on a finite set of unknown parameters, and only a set of exact relations
among the correlation functions can be derived. In the one-dimensional case we
show that by means of algebraic constraints it is possible to obtain extra
equations which close the set and allow us to obtain a complete exact solution
of the model. The behavior of the relevant physical properties for the 1D
system is reported.
