Percolation thresholds on 3-dimensional lattices with 3 nearest neighbors

TL;DR

This study investigates percolation thresholds on three-dimensional lattices with three nearest neighbors, revealing that thresholds are higher than in diamond and similar across different lattice types despite structural differences.

Contribution

It provides new data on percolation thresholds for various 3-connected lattices with different symmetries and underlying structures.

Findings

Percolation thresholds are higher than in diamond.

Thresholds are similar across different lattice types.

Structural differences beyond nearest neighbors have limited impact.

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.