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Universal Mass Ratios of Non-Unique Spanning Clusters in Percolation

Author

Listed:
  • Parongama Sen

    (Institute of Theoretical Physics, University of Cologne, Zulpicher Strasse 77, 50937 Cologne, Germany)

  • Amnon Aharony

    (School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel)

Abstract

We find that when two or more spanning clusters exist at the percolation threshold, the mass of each scales with the same fractal dimensionD=1.89in two dimensions andD=2.53in three dimensions. We also determine the ratios of the masses of the spanning clusters. In two dimensions, this is done for different lattices of different shapes. In the case of two spanning clusters, the ratio of the larger spanning cluster to the smaller lies around 1.4 for two dimensions, almost independent of lattice structure and shape.

Suggested Citation

  • Parongama Sen & Amnon Aharony, 1997. "Universal Mass Ratios of Non-Unique Spanning Clusters in Percolation," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 8(05), pages 1169-1173.
    • Handle: RePEc:wsi:ijmpcx:v:08:y:1997:i:05:n:s012918319700103x
    DOI: 10.1142/S012918319700103X
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    Keywords

    Spanning Probabilities; Fractal Dimensio;

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