The Mechanism of Localization in Weakly Coupled Disordered Grains

It is shown that the Wegner model of disorder contains a system of constraints which is important whenever the disorder is not weak and which is responsible for localization in D > 2 dimensions. When the disorder is strong the constraints divide the phase space into an exponentially large number of domains; the localized phase is a glass. This work is based on recently developed field theories which are exactly equivalent to the Wegner model and to an easier variant.