A generalized Beraha conjecture for non-planar graphs

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dc.contributor.author Jacobsen, Jesper Lykke
dc.contributor.author Salas Martínez, Jesús
dc.date.accessioned 2015-09-25T10:21:25Z
dc.date.available 2015-09-25T10:21:25Z
dc.date.issued 2013-10
dc.identifier.bibliographicCitation Nuclear Physics B. (2013) 875, 3, 678–718.
dc.identifier.issn 0550-3213
dc.identifier.uri http://hdl.handle.net/10016/21623
dc.description.abstract We study the partition function ZG(nk,k) (Q,v) of the Q -state Potts model on the family of (non-planar) generalized Petersen graphs G(nk,k). We study its zeros in the plane (Q,v) for 1≤k≤7. We also consider two specializations of ZG(nk,k), namely the chromatic polynomial PG(nk,k) (Q) (corresponding to v= –1), and the flow polynomial PhiG(nk,k) (Q) (corresponding to v= –Q). In these two cases, we study their zeros in the complex Q -plane for 1≤k≤7. We pay special attention to the accumulation loci of the corresponding zeros when n→∞. We observe that the Berker&-Kadanoff phase that is present in two-dimensional Potts models, also exists for non-planar recursive graphs. Their qualitative features are the same; but the main difference is that the role played by the Beraha numbers for planar graphs is now played by the non-negative integers for non-planar graphs. At these integer values of Q, there are massive eigenvalue cancellations, in the same way as the eigenvalue cancellations that happen at the Beraha numbers for planar graphs.
dc.format.mimetype application/pdf
dc.language.iso eng
dc.relation.hasversion https://arxiv.org/abs/1303.5210
dc.rights © Elsevier Ltd.
dc.rights Atribución-NoComercial-SinDerivadas 3.0 España
dc.rights.uri http://creativecommons.org/licenses/by-nc-sa/3.0/es/
dc.subject.other Potts model
dc.subject.other Non-planar graphs
dc.subject.other Beraha conjecture
dc.subject.other Generalized Petersen graphs
dc.subject.other Transfer matrix
dc.subject.other Berker-Kadanoff phase
dc.title A generalized Beraha conjecture for non-planar graphs
dc.type article
dc.description.status Publicado
dc.subject.eciencia Matemáticas
dc.subject.eciencia Materiales
dc.identifier.doi https://doi.org/10.1016/j.nuclphysb.2013.07.012
dc.rights.accessRights openAccess
dc.type.version acceptedVersion
dc.identifier.publicationfirstpage 678
dc.identifier.publicationissue 3
dc.identifier.publicationlastpage 718
dc.identifier.publicationtitle Nuclear Physics B
dc.identifier.publicationvolume 875
dc.identifier.uxxi AR/0000013915
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