The chemical distance distribution in percolation clusters

Shlomo Havlin, Benes Trus, George H. Weiss, Daniel Ben-Avraham

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Abstract

We study the conditional probability density p (r/l), for the geometrical distance r corresponding to a given chemical distance l for percolation clusters in two dimensions. We argue that (i) p(r/l) = A1xg exp(-axδ) where x = r/lv, g = 2.5 ± 0.3, δ = 9.8 ± 0.5, and v = 0.88 ± 0.02, and (ii) there is a relation δ = (l - v)-1 which is in good agreement with our numerical data. These results are derived by considering a special class of self-avoiding walks consisting of chains which are chemical paths (shortest paths) on critical percolation clusters.

Original languageEnglish
Pages (from-to)L247-L249
JournalJournal of Physics A: Mathematical and General
Volume18
Issue number5
DOIs
StatePublished - 1 Apr 1985

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