"RSOS models"의 두 판 사이의 차이

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Pierre Mathieu, Combinatorics of RSOS paths<br>     Every minimal model in conformal field theory can be viewed as the scaling limit of a restricted-solid-on-solid (RSOS) model at criticality. States in irreducible modules of the minimal model M(p',p) can be described combinatorially by paths that represent configurations in the corresponding RSOS model, dubbed RSOS(p',p). These paths are in one-to-one correspondence with tableaux with prescribed hook differences. For p'=2, these are tableaux with successive ranks in a prescribed interval, which are known to be related to the Bressoud paths (whose generating function is the sum side of the Andrews-Gordon identity). We show how the RSOS(2,p) paths can be directly related to these paths. Generalizing this construction, we arrive at a representation of RSOS paths in terms of generalized Bressoud paths (for p>2p'). These new paths have a simple weighting and a natural particle interpretation. This then entails a natural particle spectrum for RSOS paths, which can be interpreted in terms of the kinks and breathers of the restricted sine-Gordon model.
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Pierre Mathieu, [http://ipht.cea.fr/statcomb2009/dimers/slides/mathieu.pdf Combinatorics of RSOS paths]
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Every minimal model in conformal field theory can be viewed as the scaling limit of a restricted-solid-on-solid (RSOS) model at criticality. States in irreducible modules of the minimal model M(p',p) can be described combinatorially by paths that represent configurations in the corresponding RSOS model, dubbed RSOS(p',p). These paths are in one-to-one correspondence with tableaux with prescribed hook differences. For p'=2, these are tableaux with successive ranks in a prescribed interval, which are known to be related to the Bressoud paths (whose generating function is the sum side of the Andrews-Gordon identity). We show how the RSOS(2,p) paths can be directly related to these paths. Generalizing this construction, we arrive at a representation of RSOS paths in terms of generalized Bressoud paths (for p>2p'). These new paths have a simple weighting and a natural particle interpretation. This then entails a natural particle spectrum for RSOS paths, which can be interpreted in terms of the kinks and breathers of the restricted sine-Gordon model.
  
 
 
 
 
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* [http://dx.doi.org/10.1088/1751-8113/42/12/122001 Particles in RSOS paths]<br>
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** P Jacob and P Mathieu, 2009
 
* [http://www.springerlink.com/content/a38dkrj20anfxl2n/ An Elliptic Algebra Uq,p([^(sl2)])Uq,p(sl2︿) and the Fusion RSOS Model]<br>
 
* [http://www.springerlink.com/content/a38dkrj20anfxl2n/ An Elliptic Algebra Uq,p([^(sl2)])Uq,p(sl2︿) and the Fusion RSOS Model]<br>
 
** 1998
 
** 1998
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* http://front.math.ucdavis.edu/search?a=&t=&c=&n=40&s=Listings&q=
 
* http://front.math.ucdavis.edu/search?a=&t=&c=&n=40&s=Listings&q=
 
* http://www.ams.org/mathscinet/search/publications.html?pg4=AUCN&s4=&co4=AND&pg5=TI&s5=&co5=AND&pg6=PC&s6=&co6=AND&pg7=ALLF&co7=AND&Submit=Search&dr=all&yrop=eq&arg3=&yearRangeFirst=&yearRangeSecond=&pg8=ET&s8=All&s7=
 
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* http://dx.doi.org/
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* http://dx.doi.org/10.1088/1751-8113/42/12/122001
  
 
 
 
 

2010년 11월 27일 (토) 06:05 판

introduction
  • restricted solid-on-solid (RSOS) models
  • also called as ABF(Andrews-Baxter-Forrester models)
  • class of a spin system
  • IBF(interaction round a face) model
  • vertex counterpart is Belavin's generalization of the 8-vertex model

 

 

 

physical description
  • a rough, discrete analogon of a gently fluctutationg surface of a liquid
  • neighboring points cannot have heights which differ much from each other
  • local energy density is given by the surface energy

 

 

height variable
  • to each site i, we assign a height variable

 

 

 

Boltzmann weight

 

 

 

critical RSOS model

 

 

 

Pierre Mathieu, Combinatorics of RSOS paths

Every minimal model in conformal field theory can be viewed as the scaling limit of a restricted-solid-on-solid (RSOS) model at criticality. States in irreducible modules of the minimal model M(p',p) can be described combinatorially by paths that represent configurations in the corresponding RSOS model, dubbed RSOS(p',p). These paths are in one-to-one correspondence with tableaux with prescribed hook differences. For p'=2, these are tableaux with successive ranks in a prescribed interval, which are known to be related to the Bressoud paths (whose generating function is the sum side of the Andrews-Gordon identity). We show how the RSOS(2,p) paths can be directly related to these paths. Generalizing this construction, we arrive at a representation of RSOS paths in terms of generalized Bressoud paths (for p>2p'). These new paths have a simple weighting and a natural particle interpretation. This then entails a natural particle spectrum for RSOS paths, which can be interpreted in terms of the kinks and breathers of the restricted sine-Gordon model.

 

 

knots and links
  • [Wu1992]

 

 

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