Anomalous diffusion at percolation threshold in high dimensions on 10^18 sites

Dirk Osterkamp, Dietrich Stauffer, Amnon Aharony

Published 2003-02-03, updated 2003-02-12Version 2

Using an inverse of the standard linear congruential random number generator, large randomly occupied lattices can be visited by a random walker without having to determine the occupation status of every lattice site in advance. In seven dimensions, at the percolation threshold with L^7 sites and L < 420, we confirm the expected time-dependence of the end-to-end distance (including the corrections to the asymptotic behavior).