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 HoshenKopelman algorithm combined with Grassberger's "go with the winner" strategy for the site percolation. We carried out a finitesize 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 meanfield behavior around the upper critical dimension is also discussed.
 Publication:

Soviet Journal of Experimental and Theoretical Physics Letters
 Pub Date:
 October 2002
 DOI:
 10.1134/1.1528706
 arXiv:
 arXiv:condmat/0207605
 Bibcode:
 2002JETPL..76..475S
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Disordered Systems and Neural Networks;
 High Energy Physics  Lattice;
 Mathematical Physics
 EPrint:
 5 pages, 4 figures, 4 tables