LENGTH SCALING OF CONDUCTANCE DISTRIBUTION FOR RANDOM FRACTAL LATTICES

One can evaluate the Kubo-Greenwood conductance sum in closed form for regular fractal structures. At a Cantor set of energies, the conducta nce is independent of lattice size L. Here we study scaling with L of the conductance distribution f(g) near such special energies in the pr esence of random bond disorder. A scaling theory may apply to the aver age or median value of lng for which there is a transition from weak t o strong localization as the lattice size L exceeds a critical value L (c) that depends on disorder. Of more interest is the form of f(g) wit h random disorder. We discuss the behavior of f(g) in the weak (L < L( c)) and strong (L(c) < L) localization limits as well as in the critic al case (L similar to L(c)) where the conducting paths involve a set o f states with fractal dimension different from that of the lattice. We are able to describe the curves in terms of two parameters which do n ot depend on details of the underlying model. The resulting shape func tion describes the critical distribution as well and strong localizati on limits.