Critical Point and Percolation Probability in a Long Range Site Percolation Model on ${\mathbb{Z}}^d$

Bernardo N. B. de Lima, Rémy Sanchis, Roger W. C. Silva

Consider an independent site percolation model with parameter $p\in (0,1)$ on ${\mathbb{Z}}^d,d\ge 2$ where there are only nearest neighbor bonds and long range bonds of length $k$ paral…