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.
- Publication:
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Soviet Journal of Experimental and Theoretical Physics Letters
- Pub Date:
- October 2002
- DOI:
- 10.1134/1.1528706
- arXiv:
- arXiv:cond-mat/0207605
- Bibcode:
- 2002JETPL..76..475S
- Keywords:
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- Condensed Matter - Statistical Mechanics;
- Condensed Matter - Disordered Systems and Neural Networks;
- High Energy Physics - Lattice;
- Mathematical Physics
- E-Print:
- 5 pages, 4 figures, 4 tables