Honeycomb Lattices with Defects

TL;DR

This paper introduces a variant of honeycomb lattices with random defects created by bond exchanges, studying their percolation properties and thresholds through a novel computational approach.

Contribution

It presents a new method to generate and analyze defective honeycomb lattices with variable degree distributions for percolation studies.

Findings

Percolation thresholds are consistent with other three-coordinated lattices.

The lattices exhibit a continuum of degree distribution standard deviations.

The method enables modeling of random systems with adjustable defect levels.

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.