Surface exponent in percolation and central-force percolation: A test for splay rigidity

We study two related problems: one in the usual percolation and the other in central-force percolation; namely, the probability that a site sitting on the border of a semi-infinite domain belongs to either the infinite cluster in usual percolation or the infinitely rigid cluster in central-force percolation. We study the critical exponents describing the critical behavior of these probabilities by a numerical simulation using a transfer-matrix technique. Our results are consistent with the hypothesis that both critical phenomena belong to the same universality class. In addition, our results suggest that the splay-rigid phase threshold is different from the rigidity threshold in central-force percolation.