Monte Carlo experiments on percolation: the influence of boundary conditions

The slow convergence of the cluster size distribution observed in recent Monte Carlo simulations of two-dimensional site percolation is shown to be due to the use of free boundary conditions. When periodic boundaries are employed the convergence is improved considerably to the extent that the integrated size distribution for large (typically 10 10 site) lattices is essentially flat over a range of cluster sizes spanning three orders of magnitude. The existence of this plateau, originally predicted by scaling theory, leads to an improved estimate of the critical probability for the square lattice. The observed correction to scaling is not readily characterised by a single additive term, a fact which helps one to understand the wide range of published exponent estimates.