SCALING BEHAVIOR IN VERY SMALL PERCOLATION LATTICES

We examine the average cluster distribution as a function of lattice p robability for a very small (L = 6) lattice and determine the scaling function of three-dimensional percolation. The behavior of the second moment, calculated from the average cluster distribution of L = 6 and L = 63 lattices, is compared to power-law behavior predicted by the sc aling function. We also examine the finite-size scaling of the critica l point and the size of the largest cluster at the critical point. Thi s analysis leads to estimates of the critical exponent nu and the rati o of critical exponents beta/nu.