Exactly soluble diluted random one-dimensional lattices

Abstract

Exact solutions for the characteristic function, which determines the density of states and inverse localization length, and one-particle Green function are presented for a class of lattice models with diluted randomness. (Examples are: harmonic, electronic, relaxation and X-Y spin systems.) With probability 1 - p the random variables assume a constant value; with probability p they have values taken from an exponential distribution (diagonal disorder) or from a power-law distribution (off-diagonal disorder).