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* vertex counterpart is Belavin's generalization of the 8-vertex model | * vertex counterpart is Belavin's generalization of the 8-vertex model | ||
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==physical description== | ==physical description== | ||
| − | * a rough, discrete analogon of a gently fluctutationg surface of a liquid | + | * a rough, discrete analogon of a gently fluctutationg surface of a liquid |
| − | * neighboring points cannot have heights which differ much from each other | + | * neighboring points cannot have heights which differ much from each other |
| − | * local energy density is given by the surface energy | + | * local energy density is given by the surface energy |
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==height variable== | ==height variable== | ||
| − | * to each site i, we assign a height variable | + | * to each site i, we assign a height variable |
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==Boltzmann weight== | ==Boltzmann weight== | ||
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==critical RSOS model== | ==critical RSOS model== | ||
| − | * A_3 RSOS model = [[Ising models]] | + | * A_3 RSOS model = [[Ising models]] |
| − | * D_4 RSOS model = [[3-states Potts model]] | + | * D_4 RSOS model = [[3-states Potts model]] |
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Pierre Mathieu, [http://ipht.cea.fr/statcomb2009/dimers/slides/mathieu.pdf Combinatorics of RSOS paths] | Pierre Mathieu, [http://ipht.cea.fr/statcomb2009/dimers/slides/mathieu.pdf Combinatorics of RSOS paths] | ||
| 56번째 줄: | 56번째 줄: | ||
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. | 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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==knots and links== | ==knots and links== | ||
| − | * '''[Wu1992]''' | + | * '''[Wu1992]''' |
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==history== | ==history== | ||
| 72번째 줄: | 72번째 줄: | ||
* http://www.google.com/search?hl=en&tbs=tl:1&q= | * http://www.google.com/search?hl=en&tbs=tl:1&q= | ||
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==related items== | ==related items== | ||
| − | * [[5 conformal field theory(CFT)|conformal field theory]] | + | * [[5 conformal field theory(CFT)|conformal field theory]] |
| − | * [[minimal models]] | + | * [[minimal models]] |
| − | * [[six-vertex model and Quantum XXZ Hamiltonian]] | + | * [[six-vertex model and Quantum XXZ Hamiltonian]] |
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==articles== | ==articles== | ||
| − | * [http://dx.doi.org/10.1088/1751-8113/42/12/122001 Particles in RSOS paths] | + | * [http://dx.doi.org/10.1088/1751-8113/42/12/122001 Particles in RSOS paths] |
** P Jacob and P Mathieu, 2009 | ** P Jacob and P Mathieu, 2009 | ||
| − | * [http://dx.doi.org/10.1063/1.3157921 Paths and partitions: Combinatorial descriptions of the parafermionic states] | + | * [http://dx.doi.org/10.1063/1.3157921 Paths and partitions: Combinatorial descriptions of the parafermionic states] |
** Pierre Mathieu, J. Math. Phys. 50, 095210 (2009) | ** Pierre Mathieu, J. Math. Phys. 50, 095210 (2009) | ||
| − | * [http://www.springerlink.com/content/a38dkrj20anfxl2n/ An Elliptic Algebra Uq,p([^(sl2)])Uq,p(sl2︿) and the Fusion RSOS Model] | + | * [http://www.springerlink.com/content/a38dkrj20anfxl2n/ An Elliptic Algebra Uq,p([^(sl2)])Uq,p(sl2︿) and the Fusion RSOS Model] |
** 1998 | ** 1998 | ||
| − | * http://www.iop.org/EJ/article/0305-4470/28/15/014/ja951514.pdf?request-id=532771e8-0c58-4207-91d0-f7f1a3005871 | + | * http://www.iop.org/EJ/article/0305-4470/28/15/014/ja951514.pdf?request-id=532771e8-0c58-4207-91d0-f7f1a3005871 |
** 1995 | ** 1995 | ||
| − | * '''[Wu1992]'''[http://www.physics.neu.edu/faculty/wu%20files/pdf/Wu152_RMP64_1099.pdf Knot theory and statistical mechanics.] | + | * '''[Wu1992]'''[http://www.physics.neu.edu/faculty/wu%20files/pdf/Wu152_RMP64_1099.pdf Knot theory and statistical mechanics.] |
** F. Y. Wu, Rev. Mod. Phys. 64, 1099 (1992) | ** F. Y. Wu, Rev. Mod. Phys. 64, 1099 (1992) | ||
| − | * [http://dx.doi.org/10.1016/0378-4371%2892%2990149-K Conformal weights of RSOS lattice models and their fusion hierarchies] | + | * [http://dx.doi.org/10.1016/0378-4371%2892%2990149-K Conformal weights of RSOS lattice models and their fusion hierarchies] |
** Klümper, Andreas; Pearce, Paul A., 1992 | ** Klümper, Andreas; Pearce, Paul A., 1992 | ||
| − | * [http://dx.doi.org/10.1088/0305-4470/23/9/012 Restricted solid-on-solid models connected with simply laced algebras and conformal field theory] | + | * [http://dx.doi.org/10.1088/0305-4470/23/9/012 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 | ** V. Bazhanov, N. Reshetikhin, 1990 J. Phys. A: Math. Gen. 23 1477 | ||
| − | * [http://dx.doi.org/10.1142/S0217751X89000042 Critical RSOS models and conformal field theory] | + | * [http://dx.doi.org/10.1142/S0217751X89000042 Critical RSOS models and conformal field theory] |
** V. Bazhanov, N. Reshetikhin, 1988 | ** V. Bazhanov, N. Reshetikhin, 1988 | ||
| − | * [http://www.sciencedirect.com/science?_ob=MiamiImageURL&_imagekey=B6TVC-4719S7Y-26T-3&_cdi=5531&_user=4420&_check=y&_orig=search&_coverDate=12%2F31%2F1987&view=c&wchp=dGLbVlW-zSkWz&md5=bbff7c5b006ff5e8c44c75ac96bbb527&ie=/sdarticle.pdf Exactly solvable SOS models. Local height probabilities and theta function identities] | + | * [http://www.sciencedirect.com/science?_ob=MiamiImageURL&_imagekey=B6TVC-4719S7Y-26T-3&_cdi=5531&_user=4420&_check=y&_orig=search&_coverDate=12%2F31%2F1987&view=c&wchp=dGLbVlW-zSkWz&md5=bbff7c5b006ff5e8c44c75ac96bbb527&ie=/sdarticle.pdf Exactly solvable SOS models. Local height probabilities and theta function identities] |
| − | ** E. Date, M. Jimbo, A. Kuniba, T. Miwa and M. Okado, | + | ** E. Date, M. Jimbo, A. Kuniba, T. Miwa and M. Okado, <em style="line-height: 2em;">Nucl. Phys. B</em> '''290''' (1987), p. 231. |
| − | * | + | * Huse, David A. 1984. “Exact Exponents for Infinitely Many New Multicritical Points.” Physical Review B 30 (7) (October 1): 3908–3915. doi:10.1103/PhysRevB.30.3908. |
| − | + | * George E. Andrews, R. J. Baxter and P. J. Forrester [http://www.springerlink.com/content/r522x4086p54u438/ Eight-vertex SOS model and | |
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[[분류:개인노트]] | [[분류:개인노트]] | ||
[[분류:integrable systems]] | [[분류:integrable systems]] | ||
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[[분류:math and physics]] | [[분류:math and physics]] | ||
2013년 6월 21일 (금) 14:51 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
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.
- Huse, David A. 1984. “Exact Exponents for Infinitely Many New Multicritical Points.” Physical Review B 30 (7) (October 1): 3908–3915. doi:10.1103/PhysRevB.30.3908.
- George E. Andrews, R. J. Baxter and P. J. Forrester [http://www.springerlink.com/content/r522x4086p54u438/ Eight-vertex SOS model and