A computer-simulation study of anomalous diffusion on percolating clusters near to the critical point

We have verified the scaling hypothesis for the following quantities via a computer simulation: the average probability density P(r,t,Δp) r2(t) −df/2F(√z), the diffusion coefficient D(r,t,Δp) t2/dw−1h(t/τ)D0(z) and the mean-square displacement (MSD) r2(t) t2/dwf2(t/τ), where z = r2/ r2(t) . It was found that there exists a cross-over value zc, which divides interval z in two regions, where the diffusion coefficient exhibits a power-law dependence on variable z with the different exponents. In the region z < zc this exponent depends on Δp contrary to region z> zc. On the basis of the analogy of the average probability in the asymptotic form and the mean-square displacement in the case of the self-avoiding and ordinary random walk models the relation γ = dw/(dw − 1) was derived.