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Directed-site percolation clusters: The scaling function in dimensions two to six

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Zeitschrift für Physik B Condensed Matter

Abstract

Exact series for lattices of dimension between 2 and 6 are used to report on the asymptotic features of the scaling function for the average number of clusters in directed percolation, close to, and away from, the most recent estimated intervals forp c . Scanning of the noncritical regions yields exponent ranges compatible with the undirected percolation equivalents. Close top c the scaling function varies fairly linearly in terms of the variablez=(p−p c )s σ and this result is rather stable particularly bearing in mind the modestly available precision forp c in higher dimensionalities.

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Authors and Affiliations

  1. Departamento de Física, Universidade de Aveiro, P-3800, Aveiro, Portugal

    M. C. T. P. Carvalho

  2. Departamento de Física, Faculdade de Ciências do Porto, P-4000, Porto, Portugal

    J. A. M. S. Duarte

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  1. M. C. T. P. Carvalho
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  2. J. A. M. S. Duarte
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Carvalho, M.C.T.P., Duarte, J.A.M.S. Directed-site percolation clusters: The scaling function in dimensions two to six. Z. Physik B - Condensed Matter 70, 203–208 (1988). https://doi.org/10.1007/BF01318300

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  • DOI: https://doi.org/10.1007/BF01318300

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