Number of Spanning Clusters at the High-Dimensional Percolation Thresholds

Santo Fortunate, Amnon Aharony, Antonio Coniglio, Dietrich Stauffer

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

A scaling theory to derive the dependence of the average number <k> of spanning clusters at the high-dimensional percolation threshold was presented. It was found that the average number <k> 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.

Original languageEnglish
Article number056116
Number of pages7
JournalPhysical Review E
Volume70
Issue number5
DOIs
StatePublished - 1 Nov 2004

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