Small-World Bonds and Patchy Percolation on the Hanoi Network
Abstract
The bond-percolation properties of the Hanoi networks are analyzed with the renormalization group. Unlike scale-free networks, they are meant to provide an analytically tractable interpolation between finite dimensional, lattice-based models and their mean-field limits. In percolation, the hierarchical small-world bonds in the Hanoi networks impose a new form of order by uniting otherwise disconnected, local clusters. This "patchy" order results in merely a finite probability to obtain a spanning cluster for certain ranges of the bond probability, unlike the usual 0-1 transition found on ordinary lattices. The various networks studied here exhibit a range of phase behaviors, depending on the prevalence of those long-range bonds. Fixed points in general exhibit non-universal behavior.
Cite
@article{arxiv.0907.2717,
title = {Small-World Bonds and Patchy Percolation on the Hanoi Network},
author = {S. Boettcher and J. L. Cook and R. M. Ziff},
journal= {arXiv preprint arXiv:0907.2717},
year = {2009}
}
Comments
12 pages, revtex, 15 figures, find related papers at http://www.physics.emory.edu/faculty/boettcher/