Critical Percolation Probabilities for the Next-Nearest-Neighbouring Site Problems on Sierpinski Carpets

In this paper, we compute the next-nearest-neighbouring site percolation (Connections exist not only between nearest-neighbouring sites, but also between next-nearest-neighbouring sites.) probabilities on the two-dimensional Sierpinski carpets, using the translational-dilation method and Monte Carlo technique. We obtain a relation among , fractal dimensionality and connectivity . For the family of carpets with central cutouts, , where , the critical percolation probability for the next-nearest-neighbouring site problem on square lattice. As reaches , which is in agreement with the critical percolation probability on square lattices with next-nearest-neighbouring interactions.