title: Upper transition point for percolation on the enhanced binary tree: a sharpened lower bound.
abstract: Hyperbolic structures are obtained by tiling a hyperbolic surface with negative Gaussian curvature. These structures generally exhibit two percolation transitions: a system-wide connection can be established at a certain occupation probability p = pc1, and there emerges a unique giant cluster at pc2 > pc1. There have been debates about locating the upper transition point of a prototypical hyperbolic structure called the enhanced binary tree (EBT), which is constructed by adding loops to a binary tree. This work presents its lower bound as pc2 ≳ 0.55 by using phenomenological renormalization-group methods and discusses some solvable models related to the EBT.
authors.affiliation: School of Physics, Korea Institute for Advanced Study, Seoul 130-722, Korea. seungki@kias.re.kr
authors.forename: Seung Ki
authors.initials: SK
authors.lastname: Baek