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

Abstract

In this paper, we compute the next-nearest-neighboring site percolation (Connections exist not only between nearest-neighboring sites, but also between next-nearest-neighboring sites.) probabilities Pc on the two-dimensional Sierpinski carpets, using the translational-dilation method and Monte Carlo technique. We obtain a relation among Pc, fractal dimensionality D and connectivity Q. For the family of carpets with central cutouts,, where, the critical percolation probability for the next-nearest-neighboring site problem on square lattice. As D reaches 2, which is in agreement with the critical percolation probability on 2-d square lattices with next-nearest-neighboring interactions.