Diffusivity and radius of random animals, percolation clusters and compact clusters

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Abstract
Defines a cluster diffusivity Ds by introducing a random rearrangement between arbitrary cluster and perimeter sites such that the cluster remains connected. Monte Carlo simulation is used on the square and simple cubic lattices to determine the dependence of Ds and the radius of gyration Rs on s, the number of cluster sites. Three limiting cases are considered: random animals (p=0), percolation clusters (p=pc) and compact clusters (p>pc). The results for the exponent rho of Rs are consistent with the best experimental and theoretical values. The authors develop an elementary scaling theory for the observed power law dependence of Ds in terms of different mechanisms dominant for small and large clusters. A position space renormalisation group calculation in two dimensions yields corrections to the elementary theory for random animals and percolation clusters; the predictions are consistent with the Monte Carlo results for Ds.