Averaged Green's functions of discrete disordered systems from effective energy-dependent probability distributions

In a discrete disordered system one is interested in computing the averaged Green's function [G(ij)]. Using the supersymmetry formulation as a startin g point, we derive a renormalization group flow equation for the effective probability distribution of a subsystem of fu;ed size, which preserves [G(i j)], as the size of the total system is increased. From this flow equation, averaged Green's functions can be computed directly in the thermodynamic l imit, which enables us to compute the density of states and investigate loc alization/delocalization transitions. As an illustration, we consider the o ne-dimensional tight-binding Anderson model with Lorentz disorder. (C) 1999 Elsevier Science B.V. All rights reserved.