  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.
