LOCALIZATION IN A STRONGLY DISORDERED SYSTEM: A PERTURBATION APPROACH

Abstract

We prove that a strongly disordered two-dimensional system localizes with a localization length given analytically. We get a scaling law with a critical exponent ν = 1 in agreement with the Chayes criterion ν ≥ 1. The case we are considering is for off-diagonal disorder. The method we use is a perturbation approach holding in the limit of an infinitely large perturbation as recently devised and the Anderson model is considered with a Gaussian distribution of disorder. The localization length diverges when energy goes to zero with a scaling law in agreement to numerical and theoretical expectations.