  The coherent potential approximation, CPA, is a useful tool to treat systems
with disorder. Cluster theories have been proposed to go beyond the translation
invariant single-site CPA approximation and include some short range
correlations. In this framework one can also treat simultaneously diagonal
disorder (in the site-diagonal elements of the Hamiltonian) and non-diagonal
disorder (in the bond energies). It proves difficult to obtain reasonable
results, free of non-analyticities, for lattices of dimension higher than one
(D>1). We show electronic structure results obtained for a Hubbard model,
treated in mean field approximation, on a square lattice and a simple cubic
lattice, with the simultaneous inclusion of diagonal and non-diagonal disorder.
We compare the results obtained using three different methods to treat the
problem: a self-consistent 2-site cluster CPA method, the
Blackman-Esterling-Berk single-site like extension of the CPA and a nested CPA
approach.
