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dc.contributor.authorGrimmett, Geoffreyen
dc.contributor.authorLi, Zen
dc.date.accessioned2017-07-05T12:44:19Z
dc.date.available2017-07-05T12:44:19Z
dc.identifier.issn1073-7928
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/265191
dc.description.abstractThe 1-2 model on the hexagonal lattice is a model of statistical mechanics in which each vertex is constrained to have degree either 1 or 2. There are three edge directions, and three corresponding parameters a, b, c. It is proved that, when a ≥ b ≥ c >0 , the surface given by √a=√b+√c is critical. The proof hinges upon a representation of the partition function in terms of that of a certain dimer model. This dimer model may be studied via the Pfaffian representation of Fisher, Kasteleyn, and Temperley. It is proved, in addition, that the two-edge correlation function converges exponentially fast with distance when √a≠√b+√c. Many of the results may be extended to periodic models.
dc.description.sponsorshipThis work was supported in part by the Engineering and Physical Sciences Research Council under grant EP/I03372X/1. Z.L.’s research was supported by the Simons Foundation grant # 351813 and National Science Foundation DMS-1608896. We thank the referee for a detailed and useful report.
dc.languageengen
dc.language.isoenen
dc.publisherOxford University Press
dc.subject82B20en
dc.subject60K35en
dc.subject05C70en
dc.titleCritical surface of the 1-2 modelen
dc.typeArticle
prism.publicationNameInternational Mathematics Research Noticesen
dc.identifier.doi10.17863/CAM.11247
dcterms.dateAccepted2017-02-28en
rioxxterms.versionofrecord10.1093/imrn/rnx066en
rioxxterms.versionAMen
rioxxterms.licenseref.urihttp://www.rioxx.net/licenses/all-rights-reserveden
rioxxterms.licenseref.startdate2017-02-28en
dc.contributor.orcidGrimmett, Geoffrey [0000-0001-7646-3368]
dc.identifier.eissn1687-0247
rioxxterms.typeJournal Article/Reviewen
pubs.funder-project-idEPSRC (EP/I03372X/1)
cam.issuedOnline2017-04-29en
rioxxterms.freetoread.startdate2018-04-29


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