On the theory of localization in disordered systems

A localization criterion is derived by using the self-consistent determination of the self-energy in the discussion of the convergence of the Green function renormalized perturbation expansion. This criterion depends on the dimensionality and the connectivity of the lattice. It yields localization for all states in one-dimension systems and tends to the Economon-Cohen criterion when the number of neighbours tends to infinity. Moreover, one can show that delocalization occurs when the width of the probability distribution of the self-energy is of the order of magnitude of the hopping integral.