Thresholds of percolating systems with two symmetric forbidden zones having a constant separation


In this paper, we investigate the percolation thresholds for a two-dimensional system with two square banned sites, its topological equivalence with another system with a single square banned site, and the scaling property between their thresholds. An eight-corner check algorithm was implemented to evaluate the percolation of this dual banned sites system. We found that percolation threshold for the dual case follows the same trend as the single case, where the threshold increases as the banned site dimension (X) is increased. Our results suggest that the thresholds for the single and dual case are related by some finite scaling laws.