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arXiv · 1111.3254

Simple cubic random-site percolation thresholds for complex neighbourhoods

Lukasz Kurzawski·Krzysztof Malarz
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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.

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Lukasz Kurzawski, Krzysztof Malarz. 2011-11-14. Simple cubic random-site percolation thresholds for complex neighbourhoods. https://doi.org/10.1016/s0034-4877(12)60036-6

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