Percolation thresholds on 3-dimensional lattices with 3 nearest neighbors

Abstract

We present a study of site and bond percolation on periodic lattices with 3 nearest neighbors per site. We have considered 3 lattices, with different symmetries, different underlying Bravais lattices, and different degrees of longer-range connections. As expected, we find that the site and bond percolation thresholds in all of the 3-connected lattices studied here are significantly higher than in diamond. Interestingly, thresholds for different lattices are similar to within a few percent, despite the differences between the lattices at scales beyond nearest and next-nearest neighbors.