DENSITY PROFILE OF THE INCIPIENT INFINITE PERCOLATION CLUSTER

Dietrich Stauffer () and Amnon Aharony ()
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Dietrich Stauffer: School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel;
Amnon Aharony: Institute for Theoretical Physics, Cologne University, D-50923 Köln, Euroland, Germany

International Journal of Modern Physics C (IJMPC), 1999, vol. 10, issue 05, 935-940

Abstract: Monte Carlo simulations show simple scaling for the number of sites in the spanning cluster at the percolation threshold as a function of distance from the border. The results for free boundary conditions represent crossover from surface to bulk fractal dimensions, and the former agrees with exact results ind=2andd=6-∊dimensions and with earlier simulations. We also present and explain results for bus–bar boundary conditions, with two types of connection rules. The scaling functions, which are predicted to be universal, surprisingly seem not to depend on the aspect ratios of the samples.

Keywords: Connectivity function; Critical exponents; Dimensionality dependence (search for similar items in EconPapers)
Date: 1999
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DOI: 10.1142/S0129183199000735

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