Reviews of Modern Physics, Vol. 66, No. 2, pp. 261-380, April 1994

## The Anderson-Mott Transition

### by D. Belitz and T.R. Kirkpatrick

The interacting disordered electron problem is reviewed with emphasis on the
quantum phase transitions that occur in a model system and on the
field-theoretic methods used to describe them. An elementary discussion of
conservation laws and diffusive dynamics is followed by a detailed
derivation of the extended nonlinear sigma model, which serves as an
effective field theory for the problem. A general scaling theory of
metal-insulator and related transitions is developed, and explicit
renormalization-group calculations for the various universality classes
are reviewed and compared with experimental results. A discussion of
pertinent physical ideas and phenomenological approaches to the
metal-insulator transition not contained in the sigma model approach is
given, and phase transition aspects of related problems, like disordered
superconductors and the quantum Hall effect, are discussed. The review
concludes with a list of open problems.
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