Simple cubic random-site percolation thresholds for complex neighbourhoods
Abstract
In this communication with computer simulation we evaluate simple cubic random-site percolation thresholds for neighbourhoods including the nearest neighbours (NN), the next-nearest neighbours (2NN) and the next-next-nearest neighbours (3NN). Our estimations base on finite-size scaling analysis of the percolation probability vs. site occupation probability plots. The Hoshen--Kopelman algorithm has been applied for cluster labelling. The calculated thresholds are 0.1372(1), 0.1420(1), 0.0976(1), 0.1991(1), 0.1036(1), 0.2455(1) for (NN + 2NN), (NN + 3NN), (NN + 2NN + 3NN), 2NN, (2NN + 3NN), 3NN neighbourhoods, respectively. In contrast to the results obtained for a square lattice the calculated percolation thresholds decrease monotonically with the site coordination number z, at least for our inspected neighbourhoods.
Cite
@article{arxiv.1111.3254,
title = {Simple cubic random-site percolation thresholds for complex neighbourhoods},
author = {Lukasz Kurzawski and Krzysztof Malarz},
journal= {arXiv preprint arXiv:1111.3254},
year = {2012}
}
Comments
presented at SigmaPhi2011 conference