Effect of Dimensionality on the Percolation Thresholds of Various $d$-Dimensional Lattices

Salvatore Torquato, Yang Jiao

We show analytically that the $[0,1]$, $[1,1]$ and $[2,1]$ Pad{é} approximants of the mean cluster number $S(p)$ for site and bond percolation on general $d$-dimensional lattices a…