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.

Authors: Havlin S, Ben-Avraham D, Sompolinsky H.
Year of publication: 1983
Journal: Physical Review A 27(3) · March 1983

Link to publication:


“Working memory”