DISORDERED SYSTEM WITH N-ORBITALS PER SITE - 1-N EXPANSION

Averaged Green's functions for a disordered electronic system with n 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 dimensionality d>2 and diverge as d 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 finite n and d=2 in one of our models. Critical exponents for d infinitesimal above two are given. In this limit v 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 the n=∞ limit. Diagrams with s loops contribute in order n-s. 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 for d>2. © 1979 Springer-Verlag.