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 ⅔, 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%.