Amplitude ratios and β estimates from general dimension percolation moments

Joan Adlert, Amnon Aharony, Yigal Meir, A. Brooks Harrist

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Low concentration series are generated for moments of the percolation cluster size distribution, Tj=(sJ-') (s is the number of sites on a cluster) for j = 2,…, 8 and general dimensionality d. These diverge at pcas (FORMULA PRESENTED.), where (FORMULA PRESENTED.) is the gap exponent. The series yield new accurate values for Δand βΔ = 2.23 ± 0.05, 2.10 ± 0.04, 2.03 ± 0.05 and 946; = 0.44 ± 0.15, 0.66 ± 0.09, 0.83 ± 0.08 at d = 3, 4, 5. In addition, ratios of the form AjAk/AmAn„, with j+ k = m + n, are shown to be universal. New values for some of these ratios are evaluated from the series, from the e expansion (έ = 6 — d) and exactly (in d = 1 and on the Bethe lattice). The results are in excellent agreement with each other for all dimensions. Results for different lattices at d = 2, 3 agree very well. These amplitude ratios are much better behaved than other ratios considered in the past, and should thus be more useful in characterising percolating systems.

Original languageEnglish
Pages (from-to)3631-3643
Number of pages13
JournalJournal of Physics A: Mathematical and General
Issue number17
StatePublished - 1 Dec 1986


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