MONTE-CARLO SIMULATION OF LONG-TIME PERCOLATION DIFFUSION ON D=2 LATTICES ABOVE THE THRESHOLD

Monte Carlo simulations of percolation diffusion at and below the perc olation threshold give results in accordance with theory. Above the pe rcolation threshold, however, this is not the case. It was thought tha t above the threshold a well-defined crossover point separated the ano malous and classical diffusion regimes, with the classical diffusion c oefficient having the same critical exponent as the lattice conductivi ty, but Monte Carlo simulations failed to confirm this expected behavi our. Analysis of new Monte Carlo results presented here for the square lattice shows that percolation diffusion is classical only strictly a symptotically. Instead of a crossover, the approach to classical behav iour is better described as a very slow relaxation. Accounting for thi s relaxation enables the critical behaviour of percolation diffusion t o be confirmed with a corresponding critical exponent mu = 1.291 +/- 0 .024.