Reply to Comment on `Monte-Carlo simulation study of the two-stage percolation transition in enhanced binary trees'

Abstract

We discuss the nature of the two-stage percolation transition on the enhanced binary tree in order to explain the disagreement in the estimation of the second transition probability between the one in our recent paper (J. Phys. A:Math. Theor. 42 (2009) 145001) and the one in the comment to it from Baek, Minnhagen and Kim. We point out some reasons that the finite size scaling analysis used by them is not proper for the enhanced tree due to its nonamenable nature, which is verified by some numerical results.

5 pages, 4 figures

References in corpus (4)

• Percolation in the Hyperbolic Plane
• Percolation on hyperbolic lattices
• Monte-Carlo simulation study of the two-stage percolation transition in enhanced binary trees
• Comment on `Monte Carlo simulation study of the two-stage percolation transition in enhanced binary trees'

Cited by in corpus (8)

• Generating-function approach for bond percolations in hierarchical networks
• Transition-type change between an inverted Berezinskii-Kosterlitz-Thouless transition and an abrupt transition in the bond percolation on a random hierarchical small-world network
• Crossing on hyperbolic lattices
• Critical Phase of Bond Percolations on Growing Networks
• Criticality governed by the stable renormalization fixed point of the Ising model in the hierarchical small-world network
• Analytic results for the percolation transitions of the enhanced binary tree
• Bounds of percolation thresholds in the enhanced binary tree
• Bounds of percolation thresholds on hyperbolic lattices