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

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

• conformal field theory
• minimal models
• six-vertex model and Quantum XXZ Hamiltonian

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)
• ==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

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

• conformal field theory
• minimal models
• six-vertex model and Quantum XXZ Hamiltonian

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
• Pearce, Paul A., and Bernard Nienhuis. 1998. “Scaling Limit of RSOS Lattice Models and TBA Equations.” Nuclear Physics B 519 (3) (May 25): 579–596. doi:10.1016/S0550-3213(98)00134-5.
• 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)
• Klümper, Andreas, and Paul A. Pearce. 1992. “Conformal Weights of RSOS Lattice Models and Their Fusion Hierarchies.” Physica A: Statistical Mechanics and Its Applications 183 (3) (May 1): 304–350. doi:10.1016/0378-4371(92)90149-K.
• 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

• 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