"RSOS models"의 두 판 사이의 차이

2012년 10월 29일 (월) 09:53 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

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

http://www.google.com/search?hl=en&tbs=tl:1&q=

related items

encyclopedia

http://ko.wikipedia.org/wiki/
http://en.wikipedia.org/wiki/
Princeton companion to mathematics(Companion_to_Mathematics.pdf)

books

4909919

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

question and answers(Math Overflow)

blogs

구글 블로그 검색
- http://blogsearch.google.com/blogsearch?q=
- http://blogsearch.google.com/blogsearch?q=

experts on the field

http://arxiv.org/

links

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