Percolative conduction and the Alexander-Orbach conjecture in two dimensions

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.