Advertisement

Zeitschrift für Physik B Condensed Matter

, Volume 34, Issue 4, pp 327–348 | Cite as

Disordered system withn orbitals per site: 1/n expansion

  • Reinhold Oppermann
  • Franz Wegner
Article

Abstract

Averaged Green's functions for a disordered electronic system withn orbitals per site are expanded in powers of 1/n. These expansions should be valid in the region of extended states. The expansion coefficients for the d.c. conductivity are finite for dimensionalityd>2 and diverge asd approaches 2. Similarities of two types of two-particle Green's functions with the transverse and longitudinal susceptibilities of a ferromagnet with broken continuous symmetry are pointed out. Arguments for two being the lower critical dimensionality for the hydrodynamics and the mobility edge are given. Provided our series can be exponentiated we find that no metallic conductivity exists for finiten andd=2 in one of our models. Critical exponents ford infinitesimal above two are given. In this limitv diverges like 1/(d−2) and the conductivity vanishes linearly at the mobility edge.

The diagrams of the Green's functions are given in terms of vertices of short-range order and of the two-particle propagators of then=∞ limit. Diagrams withs loops contribute in orderns. The diagrams can be rearranged so that a number of vertices vanishes like the square of the wavevector. This feature prevents infrared divergencies for the d.c. conductivity ford>2.

Keywords

Neural Network Complex System Nonlinear Dynamics Expansion Coefficient Electronic System 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Wegner, F.J.: Phys. Rev. B19, 783 (1979)Google Scholar
  2. 2.
    Langer, J.S., Neal, T.: Phys. Rev. Lett.16, 984 (1966)Google Scholar
  3. 3.
    Brézin, E., Le Guillou, J.C., Zinn-Justin, J.: Domb, C., Green, M.S.: Phase Transitions and Critical Phenomena, Vol. 6, London, New York: Academic Press 1976Google Scholar
  4. 4.
    Bronk, B.V.: J. Math. Phys.5, 215 (1964)Google Scholar
  5. 5.
    Metha, M.L.: Random Matrices and the Statistical Theory of Energy Levels, London, New York: Academic Press 1967Google Scholar
  6. 6.
    Theodorou, G., Cohen, M.H.: Phys. Rev. B13, 4597 (1976)Google Scholar
  7. 7.
    Eggarter, T.P., Riedinger, R.: Phys. Rev. B18, 569 (1978)Google Scholar
  8. 8.
    Patashinskii, A.Z., Pokrovskii, V.L.: Sov. Phys. JETP37, 733 (1973)Google Scholar
  9. 9.
    Schäfer, L., Horner, H.: Z. Physik B29, 251 (1978) and references cited thereinGoogle Scholar
  10. 10.
    Lebowitz, J.L., Penrose, O.: Phys. Rev. Lett.35, 549 (1975) and references cited thereinGoogle Scholar
  11. 11.
    Asano, T.: Phys. Rev. Lett.24, 1409 (1970)Google Scholar
  12. 12.
    Harris, A.B.: Phys. Lett.33 A, 161 (1970)Google Scholar
  13. 13.
    Hikami, S., Brezin, E.: J. Phys. A11, 1141 (1978)Google Scholar
  14. 14.
    Velicky, B.: Phys. Rev.184, 614 (1969)Google Scholar
  15. 15.
    Aharony, A., Imry, Y.: J. Phys. C10, L487 (1977)Google Scholar
  16. 16.
    Polyakov, A.M.: Phys. Lett. B59, 79 (1975)Google Scholar
  17. 17.
    Migdal, A.A.: Sov. Phys. JETP42, 743 (1976)Google Scholar
  18. 18.
    Brézin, E., Zinn-Justin, J.: Phys. Rev. Lett.36, 691 (1976)Google Scholar
  19. 19.
    Brézin, E., Zinn-Justin, J.: Phys. Rev. B14, 3110 (1976)Google Scholar
  20. 20.
    Götze, W.: Solid State Commun.27, 1393 (1978)Google Scholar
  21. 21.
    Götze, W.: J. Phys. C12, 1279 (1979)Google Scholar
  22. 22.
    Götze, W., Prelovšek, P., Wölfle, P.: Solid State Commun.30, 369 (1979)Google Scholar
  23. 23.
    Abrahams, E., Anderson, P.W., Licciardello, D.C., Ramakrishnan, T.V.: Phys. Rev. Lett.42, 673 (1979)Google Scholar
  24. 24.
    Mott, N.F.: Phil. Mag.26, 1015 (1972)Google Scholar
  25. 25.
    Licciardello, D.C., Thouless, D.J.: Phys. Rev. Lett.35, 1475 (1975)Google Scholar
  26. 26.
    Wegner, F.J.: Z. Physik B25, 327 (1976)Google Scholar
  27. 27.
    Schuster, H.G.: Z. Physik B31, 99 (1978)Google Scholar
  28. 28.
    Green, M.S.: J. Chem. Phys.19, 1036 (1951)Google Scholar
  29. 29.
    Kubo, R.: J. Phys. Soc. Japan12, 570 (1957)Google Scholar
  30. 30.
    Alder, B.J., Wainright, T.E.: J. Phys. Soc. Japan (Suppl.)26, 267 (1968); Phys. Rev. Lett.18, 988 (1969)Google Scholar
  31. 31.
    Pomeau, Y.: Phys. Lett.27 A, 601 (1968)Google Scholar
  32. 32.
    Dorfman, J.R., Cohen, E.G.D.: Phys. Rev. Lett.25, 1257 (1970)Google Scholar
  33. 33.
    Ernst, M.H., Hauge, E.H., van Leeuwen, J.M.: Phys. Rev. Lett.25, 1254 (1970)Google Scholar
  34. 34.
    Kawasaki, K.: Phys. Lett.34 A, 12 (1971)Google Scholar
  35. 35.
    Prelovšek, P.: Phys. Rev. Lett.40, 1596 (1978)Google Scholar
  36. 36.
    Prelovšek, P.: Phys. Rev. B18, 3657 (1978)Google Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • Reinhold Oppermann
    • 1
  • Franz Wegner
    • 1
  1. 1.Institut für Theoretische PhysikUniversität HeidelbergHeidelberg 1Germany

Personalised recommendations