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Aperiodic non-isomorphic lattices with equivalent percolation and random-cluster models
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2010 (English)In: The Electronic Journal of Combinatorics, ISSN 1097-1440, E-ISSN 1077-8926, Vol. 17, no 1Article in journal (Refereed) Published
Abstract [en]

We explicitly construct an uncountable class of infinite a periodic plane graphs which have equal, and explicitly computable, bond percolation thresholds. Furt hermore for both bond percolation and the random-cluster model all large scale properties, such as the values of the percolation threshold and the critical exponents, of the graphs are equal. This equivalence holds for all values of p and all q is an element of [0,infinity] for the random-cluster model. The graphs are constructed by placing a copy of a rotor gadget graph or its reflection in each hyperedge of a connected self-dual 3-uniform plane hypergraph lattice. The exact bond percolation threshold may be explicitly determined as the root of a polynomial by using a generalised star-triangle transformation. Related randomly oriented models share the same bond percolation threshold value.

Place, publisher, year, edition, pages
2010. Vol. 17, no 1
Keyword [en]
thresholds
Identifiers
URN: urn:nbn:se:umu:diva-41322ISI: 000276048900003OAI: oai:DiVA.org:umu-41322DiVA: diva2:405613
Note
575EG Times Cited:0 Cited References Count:21Available from: 2011-03-23 Created: 2011-03-23 Last updated: 2017-12-11Bibliographically approved

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