Small-World Bonds and Patchy Percolation on the Hanoi Network

Details Small-World Bonds and Patchy Percolation on the Hanoi Network Small-World Bonds and Patchy Percolation on the Hanoi Network

2009-07-15

arxiv.org/abs/0907.2717v1

Phys. Rev. E 80 (4), 041115 (12 pages) 13 October 2009

Physics

Condensed Matter

Disordered Systems and Neural Networks

12 pages, revtex, 15 figures, find related papers at http://www.physics.emory.edu/faculty/boettcher/

Scientific paper

10.1103/PhysRevE.80.041115

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.

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