Confirmation of Dynamical Scaling at the Percolation Threshold

Abstract

In contrast to some earlier studies, good agreement has been found between the asymptotic random-walk exponent for particles restricted to the occupied sites of a simplecubic lattice, and the dynamical scaling prediction of Gefen, Aharony, and Alexander. For the first time, up to ${10}^{7}$ steps were used in the Monte Carlo study, which moreover employed larger lattices (${180}^{3}$) than earlier studies.