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Comment on `Monte Carlo simulation study of the two-stage percolation transition in enhanced binary trees'
Umeå University, Faculty of Science and Technology, Physics.
Umeå University, Faculty of Science and Technology, Physics.
BK21 Physics Research Division and Department of Energy Science, Sungkyunkwan University, Suwon 440-746, Korea.
2009 (English)In: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 42, 478001- p.Article in journal (Refereed) Published
Abstract [en]

The enhanced binary tree (EBT) is a nontransitive graph which has two percolation thresholds $p_{c1}$ and $p_{c2}$ with $p_{c1}<p_{c2}$. Our Monte Carlo study implies that the second threshold $p_{c2}$ is significantly lower than a recent claim by Nogawa and Hasegawa (J. Phys. A: Math. Theor. {\bf 42} (2009) 145001). This means that $p_{c2}$ for the EBT does not obey the duality relation for the thresholds of dual graphs $p_{c2}+\overline{p}_{c1}=1$ which is a property of a transitive, nonamenable, planar graph with one end. As in regular hyperbolic lattices, this relation instead becomes an inequality $p_{c2}+\overline{p}_{c1}<1$. We also find that the critical behavior is well described by the scaling form previously found for regular hyperbolic lattices.

Place, publisher, year, edition, pages
2009. Vol. 42, 478001- p.
Keyword [en]
percolation, hyperbolic lattice
National Category
Condensed Matter Physics
Research subject
Theoretical Physics
Identifiers
URN: urn:nbn:se:umu:diva-27692DOI: 10.1088/1751-8113/42/47/478001OAI: oai:DiVA.org:umu-27692DiVA: diva2:277111
Available from: 2009-11-16 Created: 2009-11-16 Last updated: 2017-12-12Bibliographically approved

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