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Bounds of percolation thresholds in the enhanced binary tree
Umeå University, Faculty of Science and Technology, Department of Physics.
Umeå University, Faculty of Science and Technology, Department of Physics.
2011 (English)In: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, E-ISSN 1873-2119, Vol. 390, no 8, 1447-1452 p.Article in journal (Refereed) Published
Abstract [en]

It is argued that the lower critical percolation threshold of the enhanced binary tree is bounded as $p_{c1} < 0.355~059$ by studying its subgraphs while the upper threshold is bounded both from above and below by $1/2$ according to renormalization-group arguments. We also review a correlation analysis in an earlier work, which claimed a significantly higher estimate of $p_{c2}$ than $1/2$, to show that this analysis in fact gives a consistent result with this bound. It confirms that the duality relation between critical thresholds does not hold exactly for the EBT and its dual, possibly due to the lack of transitivity.

Place, publisher, year, edition, pages
Elsevier, 2011. Vol. 390, no 8, 1447-1452 p.
Keyword [en]
percolation threshold, enhanced binary tree, hyperbolic lattice
National Category
Condensed Matter Physics
Research subject
Theoretical Physics
Identifiers
URN: urn:nbn:se:umu:diva-39227DOI: 10.1016/j.physa.2010.12.030OAI: oai:DiVA.org:umu-39227DiVA: diva2:388591
Funder
Swedish Research Council, 621-2002-4135
Available from: 2011-01-18 Created: 2011-01-18 Last updated: 2017-12-11Bibliographically approved

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Baek, Seung KiMinnhagen, Petter
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CiteExportLink to record
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Citation style
  • apa
  • ieee
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  • Other style
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  • de-DE
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Output format
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