Anderson Localization and Nonlinear σ Model

Abstract

An explanation of the Anderson localization in terms of the nonlinear σ model is presented. The critical behaviors of the Anderson transition between an insulator and a conductor are considered by the renormalization group treatment in 2 + ε dimensions and it is shown that these are described by the three different nonlinear σ models depending upon space and time symmetries. The case under a strong magnetic field in two dimensions is studied for the investigation of the existence of an extended state and for the consistency with the unitary nonlinear σ model.