Exact scaling law for the fragmentation of percolation clusters: Numerical evidence

We perform large-scale numerical simulations to:generate and fragment three-dimensional bond percolation clusters on the cubic lattice. We compute very accurately the standard exponents tau and gamma, as well as an exponent phi which characterizes the binary fragmentation of the clusters. Two published scaling laws which relate phi to tau and gamma are tested. Excellent agreement is obtained with one of these relations, indicating that it is possibly exact in any dimension, while the other relation is shown to be in error.