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

References in corpus (6)

• Percolation in Hierarchical Scale-Free Nets
• Small-World Bonds and Patchy Percolation on the Hanoi Network
• Percolation on hyperbolic lattices
• Monte-Carlo simulation study of the two-stage percolation transition in enhanced binary trees
• Universal condition for critical percolation thresholds of kagome-like lattices
• Reply to Comment on `Monte-Carlo simulation study of the two-stage percolation transition in enhanced binary trees'

Cited by in corpus (1)

• Hierarchical renormalization-group study on the planar bond-percolation problem