Topological properties of percolation clusters

S. Havlin, R. Nossal

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Percolation properties, including the total cluster mass S, the shell mass B, and the linear geometrical size R, are studied as a function of the topological 'chemical distance' parameter L. All critical exponents are shown to be related to an apparently new exponent nu , defined by R approximately L v. Critical exponents are calculated exactly for percolation clusters on the Cayley tree (a model for 6D percolation), for which S approximately L2, B approximately L, and R2 approximately L. For diffusion on such clusters one finds that L3 approximately t. Numerical estimates of the exponents are obtained for other dimensions. A conjecture which relates nu to beta and nu is discussed.

Original languageEnglish
Article number007
Pages (from-to)L427-L432
JournalJournal of Physics A: Mathematical and General
Issue number8
StatePublished - 1984
Externally publishedYes


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