Scaling behavior of diffusion on percolation clusters

A scaling analysis is performed on Monte Carlo simulations of random walks on percolation clusters both above and below the threshold pc. The average diffusion constant is described by a single scaling function in which the crossover from an algebraic decay (in time) near pc to the asymptotic behavior above or below it occurs at time tcross∝|p-pc|^-(2ν-β+μ). The value of the percolation conductivity exponent μ is found to be 1.05 ±{}0.05 for two-dimensional systems and 1.5 ±{}0.1 for three dimensions.