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

Dirk Osterkamp·Dietrich Stauffer·Amnon Aharony
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Abstract

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).

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Dirk Osterkamp, Dietrich Stauffer, Amnon Aharony. 2003-02-12. Anomalous diffusion at percolation threshold in high dimensions on 10^18 sites. https://doi.org/10.1142/s0129183103005066

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