Influence of boundary conditions on the fraction of spanning clusters

We use the Hoshen-Kopelman algorithm with the Nakanashi method of recycling redundant labels to measure the fraction of spanning configurations, R(p(c )), at and near p(c), for random site percolation in two and three dimensio ns with different boundary conditions. For the square and cubic lattices we find that R(p(c)) is 0.50 and 0.28 for free edges and 0.64 (2-d) and 0.56 (3-d) for both helical and periodic boundary conditions. The error bars are of the order of +/-0.01 for these results.