On the Aizenman exponent in critical percolation
Statistical Mechanics
2009-11-07 v2 Disordered Systems and Neural Networks
High Energy Physics - Lattice
Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.cond-mat/0207605,
title = {On the Aizenman exponent in critical percolation},
author = {Lev N. Shchur and Timofey Rostunov},
journal= {arXiv preprint arXiv:cond-mat/0207605},
year = {2009}
}
Comments
5 pages, 4 figures, 4 tables