Scaling form for percolation cluster sizes and perimeters

Randomly generated clusters of sites on the triangular lattice at and just below pc, and clusters previously generated on the square lattice are analysed to determine their scaling form. The scaling forms previously introduced by several authors are related and tested for accuracy by a new, one-exponent technique involving the cluster perimeter distribution. Deviations from scaling are seen for clusters smaller than about 85 sites. The Gaussian form previously suggested is generalised slightly (by the inclusion of higher-order terms) and found to be accurate in the critical region ( epsilon nphi approximately O(1)). Nevertheless, important deviations away from the Gaussian occur for nphi greater than epsilon -1 which are consistent with the theorem of Kunz and Souillard (see Phys. Rev. Latt., vol.40, p.133 (1978)) that Pn varies as exp(-an) asymptotically, for large n.