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


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.


Neural Network Complex System Nonlinear Dynamics Expansion Coefficient Electronic System 
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Copyright information

© Springer-Verlag 1979

Authors and Affiliations

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

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