Universal Mass Ratios of Non-Unique Spanning Clusters in Percolation

Parongama Sen () and Amnon Aharony ()
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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

International Journal of Modern Physics C (IJMPC), 1997, vol. 08, issue 05, 1169-1173

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.

Keywords: Spanning Probabilities; Fractal Dimensio (search for similar items in EconPapers)
Date: 1997
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DOI: 10.1142/S012918319700103X

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