Critical conducting networks in disordered solids: ac universality from topological arguments

This paper advocates an unconventional description of charge transport processes in disordered solids, which brings together the ideas of fractal geometry, percolation theory, and topology of manifolds. We demonstrate that the basic features of ac conductivity in disordered materials as seen in various experiments are reproduced with remarkable accuracy by the conduction properties of percolating fractal networks near the threshold of percolation. The universal character of ac conductivity in three embedding dimensions is discussed in connection with the available experimental data. An important prediction of the present model is the "hyperuniversal" scaling sigma(omega)proportional to omega (1/3) for ac conduction in two dimensions.