Critical surface of the 12 model
dc.contributor.author  Grimmett, Geoffrey  en 
dc.contributor.author  Li, Z  en 
dc.date.accessioned  20170705T12:44:19Z  
dc.date.available  20170705T12:44:19Z  
dc.identifier.issn  10737928  
dc.identifier.uri  https://www.repository.cam.ac.uk/handle/1810/265191  
dc.description.abstract  The 12 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 twoedge correlation function converges exponentially fast with distance when √a≠√b+√c. Many of the results may be extended to periodic models.  
dc.description.sponsorship  This 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 DMS1608896. We thank the referee for a detailed and useful report.  
dc.language  eng  en 
dc.language.iso  en  en 
dc.publisher  Oxford University Press  
dc.subject  82B20  en 
dc.subject  60K35  en 
dc.subject  05C70  en 
dc.title  Critical surface of the 12 model  en 
dc.type  Article  
prism.publicationName  International Mathematics Research Notices  en 
dc.identifier.doi  10.17863/CAM.11247  
dcterms.dateAccepted  20170228  en 
rioxxterms.versionofrecord  10.1093/imrn/rnx066  en 
rioxxterms.version  AM  en 
rioxxterms.licenseref.uri  http://www.rioxx.net/licenses/allrightsreserved  en 
rioxxterms.licenseref.startdate  20170228  en 
dc.contributor.orcid  Grimmett, Geoffrey [0000000176463368]  
dc.identifier.eissn  16870247  
rioxxterms.type  Journal Article/Review  en 
pubs.funderprojectid  EPSRC (EP/I03372X/1)  
cam.issuedOnline  20170429  en 
rioxxterms.freetoread.startdate  20180429 
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