Percolation processes in d-dimensions
- 1 November 1976
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 9 (11) , 1899-1911
- https://doi.org/10.1088/0305-4470/9/11/015
Abstract
Series data for the mean cluster size for site mixtures on a d-dimensional simple hypercubical lattice are presented. Numerical evidence for the existence of a critical dimension for the cluster growth function and for the mean cluster size is examined and it is concluded that dc=6. Exact expansions for the mean number of clusters K(p) and the mean cluster size S(p) in powers of 1/ sigma where sigma =2d-1 and pc are derived through fifth and third order, respectively. The zeroth-order terms are the Bethe approximations.Keywords
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