@article{bc12505445f14a1bb41234a39de69a53,
title = "Number of Spanning Clusters at the High-Dimensional Percolation Thresholds",
abstract = "A scaling theory to derive the dependence of the average number of spanning clusters at the high-dimensional percolation threshold was presented. It was found that the average number should become independent of L for dimensions d<6 and vary as ln L at d=6. It was also found that the predictions for d>6 depend on the boundary conditions. The results show that simulation in six dimensions are consistent with this prediction whereas in five dimensions the average number of spanning clusters still increases as ln L even up to L=201.",
author = "Santo Fortunate and Amnon Aharony and Antonio Coniglio and Dietrich Stauffer",
note = "Funding Information: We acknowledge support from the German-Israeli Foundation and from the Humboldt Foundation, P. Grassberger and J. Adler for helpful discussion, and the computer centers of the Technion (Israel, M. Goldberg) and Julich (Germany) for time on their large computers. S.F. acknowledges the support of the DFG Forschergruppe under Grant No. FOR 339/2-1. A.C. acknowledges support from MIUR-PRIN and FIRB 2002, CRdC-AMRA, and EU Network MRTN-CT-2003-504712.",
year = "2004",
month = nov,
day = "1",
doi = "10.1103/PhysRevE.70.056116",
language = "English",
volume = "70",
journal = "Physical Review E",
issn = "2470-0045",
publisher = "American Physical Society",
number = "5",
}