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arXiv · 1403.1676

Site percolation on lattices with low average coordination numbers

Ted Y. Yoo·Jonathan Tran·Shane P. Stahlheber·Carina E. Kaainoa·Kevin Djepang·Alexander R. Small
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Abstract

We present a study of site and bond percolation on periodic lattices with (on average) fewer than three nearest neighbors per site. We have studied this issue in two contexts: By simulating oxides with a mixture of 2-coordinated and higher-coordinated sites, and by mapping site-bond percolation results onto a site model with mixed coordination number. Our results show that a conjectured power-law relationship between coordination number and site percolation threshold holds approximately if the coordination number is defined as the average number of connections available between high-coordinated sites, and suggest that the conjectured power-law relationship reflects a real phenomenon requiring further study. The solution may be to modify the power-law relationship to be an implicit formula for percolation threshold, one that takes into account aspects of the lattice beyond spatial dimension and average coordination number.

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BibTeXRIS

Ted Y. Yoo, Jonathan Tran, Shane P. Stahlheber, Carina E. Kaainoa, Kevin Djepang, Alexander R. Small. 2014-03-07. Site percolation on lattices with low average coordination numbers. https://doi.org/10.1088/1742-5468%2F2014%2F06%2Fp06014

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