On the Aizenman exponent in critical percolation

  • L. N. Shchur
  • T. Rostunov


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.

PACS numbers

64.60.Ak 64.60.Fr 


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Copyright information

© MAIK "Nauka/Interperiodica" 2002

Authors and Affiliations

  • L. N. Shchur
    • 1
  • T. Rostunov
    • 1
  1. 1.Landau Institute for Theoretical PhysicsRussian Academy of SciencesChernogolovka, Moscow regionRussia

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