Fragmentation of percolation clusters in general dimensions

The scaling behavior for binary fragmentation of critical percolation clust ers in general dimensions is investigated by Monte Carlo simulation as well as by exact series expansions. We obtain values of critical exponents lamb da and phi describing the scaling of the fragmentation rate and the distrib ution of cluster masses produced by binary fragmentation. Our results for l ambda and phi in two to nine dimensions agree with the conjectured scaling relation sigma=1+lambda-phi by Edwards and co-workers [Phys. Rev. Lett. 68, 2692 (1992); Phys. Rev. A 46, 6252 (1992)], which in turn excludes the oth er scaling relations suggested by Gouyet (for d= 2), and by Roux and Guyon [J. Phys. A 22, 3693 (1989)], where sigma id the crossover exponent for the cluster numbers in percolation theory. [S1063-651X(99)51005-2].