Square-lattice site percolation at increasing ranges of neighbor bonds
Square-lattice site percolation at increasing ranges of neighbor bonds
We report site percolation thresholds for square lattice with neighbor bonds at various increasing ranges. Using Monte Carlo techniques we found that nearest neighbors (NN), next-nearest neighbors (NNN), next-next-nearest neighbors (4N), and fifth-nearest neighbors (6N) yield the same ${p}_{c}=0.592\dots{}$. The fourth-nearest neighbors (5N) give ${p}_{c}=0.298\dots{}$. This equality is proved to …