The Mechanism of Localization in Weakly Coupled Disordered Grains

TL;DR

This paper investigates how constraints in the Wegner model of disorder lead to localization in higher dimensions, revealing that strong disorder results in a glassy localized phase with many domains.

Contribution

It identifies the role of constraints in the Wegner model and connects them to localization phenomena, providing a new understanding of disordered systems with strong disorder.

Findings

Constraints cause phase space to split into many domains at strong disorder

Localized phase behaves like a glass with many metastable states

Field theories confirm the connection between constraints and localization

Abstract

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.