Bounds of percolation thresholds in the enhanced binary tree

Details Bounds of percolation thresholds in the enhanced binary tree Bounds of percolation thresholds in the enhanced binary tree

2011-02-16

arxiv.org/abs/1102.3287v1

Physica A 390, 1447 (2011)

Physics

Condensed Matter

Statistical Mechanics

12 pages, 15 figures

Scientific paper

10.1016/j.physa.2010.12.030

By studying its subgraphs, it is argued that the lower critical percolation threshold of the enhanced binary tree (EBT) is bounded as $p_{c1} < 0.355059$, while the upper threshold is bounded both from above and below by 1/2 according to renormalization-group arguments. We also review a correlation analysis in an earlier work, which claimed a significantly higher estimate of $p_{c2}$ than 1/2, to show that this analysis in fact gives a consistent result with this bound. Our result confirms that the duality relation between critical thresholds does not hold exactly for the EBT and its dual, possibly due to the lack of transitivity.

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