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dc.contributor.authorJacobsen, Jesper Lykke-
dc.contributor.authorSalas, Jesús-
dc.identifierdoi: 10.1016/j.nuclphysb.2013.07.012-
dc.identifierissn: 0550-3213-
dc.identifier.citationNuclear Physics B 875: 678- 718 (2013)-
dc.description.abstractWe 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 ΦG(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. © 2013 Elsevier B.V.-
dc.description.sponsorshipThe research of J.L.J. was supported in part by the Agence Nationale de la Recherche (grant ANR-10-BLAN-0414: DIME) and the Institut Universitaire de France. The research of J.S. was supported in part by Spanish MINECO grants FIS2012-34379 and MTM2011-24097, and by US National Science Foundation grant PHY-0424082.-
dc.subjectBerker–Kadanoff phase-
dc.subjectTransfer matrix-
dc.subjectGeneralized Petersen graphs-
dc.subjectBeraha conjecture-
dc.subjectNon-planar graphs-
dc.subjectPotts model-
dc.titleA generalized Beraha conjecture for non-planar graphs-
dc.description.versionPeer Reviewed-
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