Universal Behavior for Bond Percolation

Abstract

We collect together results for bond percolation on various lattices from two to fourteen dimensions which, in the limit of large dimension $d$ or number of neighbors $z$, smoothly approach a randomly diluted Erdős-Rényi graph. We include new results on bond diluted hyper-sphere packs in up to nine dimensions, which show the mean coordination, excess kurtosis and skewness evolving smoothly with dimension towards the Erdős-Rényi limit.

6 pages, 5 figures