On the Aizenman exponent in critical percolation

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.

5 pages, 4 figures, 4 tables

References in corpus (3)

• Go with the Winners: a General Monte Carlo Strategy
• Percolation Threshold, Fisher Exponent, and Shortest Path Exponent for 4 and 5 Dimensions
• On the quality of random number generators with taps

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• RNGSSELIB: Program library for random number generation, SSE2 realization
• Number of spanning clusters at the high-dimensional percolation thresholds