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A metal-insulator transition as a quantum glass problem

  • T. R. Kirkpatrick
  • D. Belitzi
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 492)

Abstract

We discuss a recent mapping of the Anderson-Mott metal-insulator transition onto a random field magnet problem. The most important new idea introduced is to describe the metal-insulator transition in terms of an order parameter expansion rather than in terms of soft modes via a nonlinear sigma model. For spatial dimensions d>d c + =6 a mean field theory gives the exact critical exponents. For d=6−ε the critical exponents are identical to those for a random field Ising model. Dangerous irrelevant quantum fluctuations modify Wegner’s scaling law relating the conductivity exponent to the correlation or localization length exponent. This invalidates the bound s≧2/3 for the conductivity exponent s in d=3. We also argue that activated scaling might be relevant for describing the AMT in three-dimensional systems.

Keywords

Random Field Critical Exponent Nonlinear Sigma Model Scaling Theory Anderson Transition 
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Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • T. R. Kirkpatrick
    • 1
  • D. Belitzi
    • 2
  1. 1.Institute for Physical Science and Technology and Department of PhysicsUniversity of MarylandCollege Park
  2. 2.Department of Physics and Materials Science InstituteUniversity of OregonEugene

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