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- Title
On the Aizenman Exponent in Critical Percolation.
- Authors
Shchur, L. N.; Rostunov, T.
- Abstract
The probabilities of clusters spanning a hypercube of dimension two to seven along one axis of a percolation system under criticality were investigated numerically. We used a modified Hoshen–Kopelman algorithm combined with Grassberger’s “go with the winner” strategy for the site percolation. We carried out a finite-size analysis of the data and found that the probabilities confirm Aizenman’s proposal of the multiplicity exponent for dimensions three to five. A crossover to the mean-field behavior around the upper critical dimension is also discussed. © 2002 MAIK “Nauka / Interperiodica”.
- Subjects
CLUSTER theory (Nuclear physics); HYPERCUBES; PERCOLATION theory
- Publication
JETP Letters, 2002, Vol 76, Issue 7, p475
- ISSN
0021-3640
- Publication type
Article
- DOI
10.1134/1.1528706