Self-avoiding random walks and the two-dimensional localization theorem

Abstract

We have addressed one of the most important and basic results in disordered systems, namely the complete localization of noninteracting electrons in two dimensions even at infinitesimal disorder. We present a proof of this assertion by combining some finer aspects of the behavior of self-avoiding random walks with Anderson's original approach to localization where a renormalized perturbation expansion of self-energy, whose terms have the self-avoiding random-walk character, was analyzed. © 2006 The American Physical Society.