Integrable aspects of the scaling q-state Potts models I_ bound states and bootstrap closure

《Integrable aspects of the scaling q-state Potts models I_ bound states and bootstrap closure》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、DCPT-02/51hep-th/0208111Integrableaspectsofthescalingq-statePottsmodelsI:boundstatesandbootstrapclosurePatrickDorey1,AndrewPocklington2andRobertoTateo31,3Dept.ofMathematicalSciences,UniversityofDurham,DurhamDH13LE,UK2IFT/UNESP,InstitutodeFisicaTeorica,01405-900,SaoPaulo-SP,BrasilAbstractWedis

2、cusstheq-statePottsmodelsforq≤4,inthescalingregimesclosetotheircriticalortricriticalpoints.StartingfromthekinkS-matrixelementsproposedbyChimandZamolodchikov,thebootstrapisclosedforthescalingregionsofallcriticalpoints,andforthetricriticalpointswhen4>q≥2.Wealsonoteacuriousappearanceoftheextende

3、dlastlineofFreudenthal’smagicsquareinconnectionwiththePottsmodels.arXiv:hep-th/0208111v28Oct20021e-mail:p.e.dorey@durham.ac.uk3e-mail:roberto.tateo@durham.ac.uk1IntroductionTheq-statePottsmodelsdirectlygeneralisethemostwell-knownofalltwo-dimensionalintegrablemodels,theIsingmodel.Theyhavebeenm

4、uchstudied,bothintheirownrightasinterestingstatistical-mechanicalsystems,andbecauseoftheirrelationswithothermodels–thelimitq→1,forexample,describesbondpercolation.However,theyarebynomeanscompletelyunderstood.Inthispaperanditssequelweshalldiscussthetreatmentofthesemodelsintheframeworkofcontinu

5、umfieldtheory.Suchtechniquesareexpectedtobeapplicableinscalingregimesneartocriticalpoints,thoughfortheq-statePottsmodelssomeelementsofthetreatmentwillberatherformal,reflectingthenonlocalmannerinwhichthemodelsareinitiallydefinedonthelattice.Inthispaperwefocusonthedescriptionofthemodelsintermsofth

6、eon-shelldataprovidedbyanexactS-matrix.Anumberofyearsago,ChimandZamolodchikovproposedasetofamplitudesforthescatteringofelementarykink-likeexcitationsinthelow-temperaturephaseofthemodel[1].(AdifferenttreatmenthadpreviouslybeensuggestedbySmirnov[2],basedonquantum-groupreductionsoftheIzergin-Kore

7、pinS-matrix.InthisarticleweshallworkfromtheChim-Zamolodchikovformulation,asitmorecloselyreflectsthecontinuousnatureoftheFortuin-Kasteleyn[3]definitionofthetheoryonalattice,butwenotethattherelationshipbetweenthetwoapproacheshasrecentlybeenclarifi