Conductivity and diffusion near the percolation threshold

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Abstract
The authors consider the scaling properties of the conductivity for nonzero frequencies. They analyse the relevance of various models to descriptions of actual experimental situations. They discuss more particularly the equivalence between conduction and diffusion. In this case, they find a regime where the conductivity is proportional to the size of L of the sample, corresponding to an anomalous skin effect. This L dependence leads to a frequency-dependent conductivity different from the result of Gefen, Aharony and Alexander (1983). They finally introduce a model consisting of a two-dimensional random resistor system lying on a three-dimensional substrate made of capacitors. This might be relevant to describe a system of conducting particles deposited on a thin insulating substrate such as considered recently by Laibowitz and Gefen (1984).