RSOS models
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
- A_3 RSOS model = Ising models
- D_4 RSOS model = 3-states Potts 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]
history
encyclopedia
- http://ko.wikipedia.org/wiki/
- http://en.wikipedia.org/wiki/
- Princeton companion to mathematics(Companion_to_Mathematics.pdf)
books
- 2010년 books and articles
- http://gigapedia.info/1/
- http://gigapedia.info/1/
- http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=
articles
- Particles in RSOS paths
- P Jacob and P Mathieu, 2009
- Paths and partitions: Combinatorial descriptions of the parafermionic states
- Pierre Mathieu, J. Math. Phys. 50, 095210 (2009)
- An Elliptic Algebra Uq,p([^(sl2))Uq,p(sl2︿) and the Fusion RSOS Model]
- 1998
- http://www.iop.org/EJ/article/0305-4470/28/15/014/ja951514.pdf?request-id=532771e8-0c58-4207-91d0-f7f1a3005871
- 1995
- [Wu1992]Knot theory and statistical mechanics.
- F. Y. Wu, Rev. Mod. Phys. 64, 1099 (1992)
- Conformal weights of RSOS lattice models and their fusion hierarchies
- Klümper, Andreas; Pearce, Paul A., 1992
- Restricted solid-on-solid models connected with simply laced algebras and conformal field theory
- V. Bazhanov, N. Reshetikhin, 1990 J. Phys. A: Math. Gen. 23 1477
- Critical RSOS models and conformal field theory
- V. Bazhanov, N. Reshetikhin, 1988
- Exactly solvable SOS models. Local height probabilities and theta function identities
- E. Date, M. Jimbo, A. Kuniba, T. Miwa and M. Okado, Nucl. Phys. B 290 (1987), p. 231.
- Eight-vertex SOS model and generalized Rogers-Ramanujan-type identities
- George E. Andrews, R. J. Baxter and P. J. Forrester, Journal of Statistical PhysicsVolume 35, Numbers 3-4, 193-266,, 1984
- 논문정리
- http://www.ams.org/mathscinet
- http://www.zentralblatt-math.org/zmath/en/
- http://pythagoras0.springnote.com/
- http://math.berkeley.edu/~reb/papers/index.html[1]
- 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=
- http://dx.doi.org/10.1063/1.3157921
question and answers(Math Overflow)
blogs
experts on the field