Percolative conduction and the Alexander-Orbach conjecture in two dimensions

Abstract

Alexander and Orbach have recently proposed that the ratio of the fractal dimensionality of the incipient infinite cluster in percolation to the fractual dimensionality of a random walk on the cluster is, independent of the spatial dimensionality of the system. As a consequence, they predict that the electrical conductivity exponent t =0.9479 in two dimensions, where is the correlation-length exponent. Our numerical data, which are obtained from large-lattice finite-size scaling calculations, give a value t =0.973-0.003+0.005, in disagreement with the conjecture by 2.6%. © 1984 The American Physical Society.