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On the Aizenman exponent in critical percolation

Lev N. Shchur·Timofey Rostunov
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Abstract

The probabilities of clusters spanning a hypercube of dimensions 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.

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Lev N. Shchur, Timofey Rostunov. 2002-10-27. On the Aizenman exponent in critical percolation. https://doi.org/10.1134/1.1528706

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