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arXiv · 1512.02579

Honeycomb Lattices with Defects

Meryl A. Spencer·Robert M. Ziff
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Abstract

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.

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Meryl A. Spencer, Robert M. Ziff. 2015-12-08. Honeycomb Lattices with Defects. https://doi.org/10.1103/physreve.93.042132

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