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)


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.


Random Field Critical Exponent Nonlinear Sigma Model Scaling Theory Anderson Transition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    N.F. Mott, Metal-Insulator Transitions, Taylor & Francis (London 1990).Google Scholar
  2. [2]
    For a review, see, e.g., P. A. Lee and T. V. Ramakrishnan, Rev. Mod. Phys. 57, 287 (1985).CrossRefADSGoogle Scholar
  3. [3]
    For a review, see, e.g., D. Belitz and T. R. Kirkpatrick, Rev. Mod. Phys. 66, 261 (1994).CrossRefADSGoogle Scholar
  4. [4]
    A. M. Finkel’stein, Zh. Eksp. Teor. Fiz. 84, 168 (1983) [Sov. Phys. JETP 57, 97 (1983)].Google Scholar
  5. [5]
    F. Wegner, Z. Phys. B 35, 207 (1979).CrossRefADSGoogle Scholar
  6. [6]
    See A. B. Harris and T. C. Lubensky, Phys. Rev. 23, 2640 (1981) for an order parameter description of the Anderson transition. Wegner’s result15 for the density of states in noninteracting systems proved that the transition studied in their theory is not realized.ADSMathSciNetCrossRefGoogle Scholar
  7. [7]
    T. R. Kirkpatrick and D. Belitz, Phys. Rev. Lett. 73, 862 (1994).CrossRefADSGoogle Scholar
  8. [8]
    T. R. Kirkpatrick and D. Belitz, Phys. Rev. Lett. 74, 1178 (1995).CrossRefADSGoogle Scholar
  9. [9]
    D. Belitz and T. R. Kirkpatrick, Z. Phys. B 13, 513 (1995).CrossRefADSGoogle Scholar
  10. [10]
    D. Belitz and T. R. Kirkpatrick, Phys. Rev. B 52, 13922 (1995).CrossRefADSGoogle Scholar
  11. [11]
    G. Grinstein, Phys. Rev. Lett. 37, 944 (1976).CrossRefADSGoogle Scholar
  12. [12]
    D. S. Fisher, Phys. Rev. Lett. 56, 416 (1986)CrossRefADSGoogle Scholar
  13. [12a]
    J. Villain, J. Phys. (Paris) 46, 1843 (1985).Google Scholar
  14. [13]
    For a review, see, D. P. Belanger and A. P. Young, J. Mag. Magn. Mat. 100, 272 (1991).CrossRefADSGoogle Scholar
  15. [14]
    See, e.g., J. Zinn-Justin, Quantum Field Theory and Critical Phenomena (Clarendon, Oxford 1989).Google Scholar
  16. [15]
    See, e.g., S.-K. Ma, Modern Theory of Critical Phenomena (Benjamin, Reading, MA 1976)CrossRefGoogle Scholar
  17. [15a]
    and M. E. Fisher, in Advanced Course on Critical Phenomena, edited by F. W. Hahne (Springer, Berlin 1983), p.1CrossRefGoogle Scholar
  18. [16]
    F. Wegner, Z. Phys. B 25, 327 (1976).CrossRefADSGoogle Scholar
  19. [16]
    F. Wegner, Z. Phys. B 44, 9 (1981).CrossRefMathSciNetADSGoogle Scholar

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

Personalised recommendations