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Number of spanning clusters at the high-dimensional percolation thresholds | | Santo Fortunato
; Amnon Aharony
; Antonio Coniglio
; Dietrich Stauffer
; | | Date: |
31 Oct 2004 | | Journal: | Phys Rev E, 70 (5 Pt 2), 056116 | | Abstract: | A scaling theory is used to derive the dependence of the average number k of spanning clusters at threshold on the lattice size L. This number should become independent of L for dimensions d<6 and vary as ln L at d=6 . The predictions for d>6 depend on the boundary conditions, and the results there may vary between L(d-6) and L0. While simulations in six dimensions are consistent with this prediction [after including corrections of order ln(ln L)], in five dimensions the average number of spanning clusters still increases as ln L even up to L=201 . However, the histogram P(k) of the spanning cluster multiplicity does scale as a function of kX(L), with X(L) =1+const/L, indicating that for sufficiently large L the average k will approach a finite value: a fit of the five-dimensional multiplicity data with a constant plus a simple linear correction to scaling reproduces the data very well. Numerical simulations for d>6 and for d=4 are also presented. | | Source: | PubMed, pmid15600701 | | Other source: | [GID 227884] cond-mat/0407276 | | Services: | Forum | Review | Favorites | |
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