Change search
ReferencesLink to record
Permanent link

Direct link
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, 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
URN: urn:nbn:se:umu:diva-27692DOI: 10.1088/1751-8113/42/47/478001OAI: diva2:277111
Available from: 2009-11-16 Created: 2009-11-16 Last updated: 2009-11-23Bibliographically approved

Open Access in DiVA

fulltext(432 kB)242 downloads
File information
File name FULLTEXT01.pdfFile size 432 kBChecksum SHA-512
Type fulltextMimetype application/pdf

Other links

Publisher's full text

Search in DiVA

By author/editor
Baek, Seung KiMinnhagen, Petter
By organisation
In the same journal
Journal of Physics A: Mathematical and General
Condensed Matter Physics

Search outside of DiVA

GoogleGoogle Scholar
Total: 242 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Altmetric score

Total: 76 hits
ReferencesLink to record
Permanent link

Direct link