In this paper we introduce a variant of the honeycomb lattice in which we create defects by randomly exchanging adjacent bonds, producing a random tiling with a distribution of polygon edges. We study the percolation properties on these lattices as a function of the number of exchanged bonds using a novel computational method. We find the site and bond percolation thresholds are consistent with other three-coordinated lattices with the same standard deviation in the degree distribution of the dual; here we can produce a continuum of lattices with a range of standard deviations in the distribution. These lattices should be useful for modeling other properties of random systems as well as percolation.
@article{arxiv.1512.02579,
title = {Honeycomb Lattices with Defects},
author = {Meryl A. Spencer and Robert M. Ziff},
journal= {arXiv preprint arXiv:1512.02579},
year = {2016}
}