Bounds of percolation thresholds in the enhanced binary tree

Abstract

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.

12 pages, 15 figures

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Cited by in corpus (5)

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• Ising model on a hyperbolic plane with a boundary
• Bounds of percolation thresholds on hyperbolic lattices
• Upper transition point for percolation on the enhanced binary tree: A sharpened lower bound
• Hierarchical renormalization-group study on the planar bond-percolation problem