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Density Profile Of The Incipient Infinite Percolation Cluster

Author

Listed:
  • DIETRICH STAUFFER

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

  • AMNON AHARONY

    (Institute for Theoretical Physics, Cologne University, D-50923 Köln, Euroland, Germany)

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.

Suggested Citation

  • Dietrich Stauffer & Amnon Aharony, 1999. "Density Profile Of The Incipient Infinite Percolation Cluster," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 10(05), pages 935-940.
    • Handle: RePEc:wsi:ijmpcx:v:10:y:1999:i:05:n:s0129183199000735
    DOI: 10.1142/S0129183199000735
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