Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Hexagon and pentagon identities for the Z3 Potts model

Shijong Ryang

Published Apr 15, 1991• 0 citations
Publisher

Abstract

Investigating the transformation properties of the conformal blocks in the ${Z}_{3}$ Potts model we derive some braid matrices. From the obtained braid matrices we explicitly show how the hexagon and pentagon identities are satisfied.

DOI
10.1103/physrevd.43.2745

Related papers

Braiding Diagrams

Steven H. Simon

Abstract We continue the development of diagrammatics now considering diagrams living in 3 dimensions. We generalize the discussion of the R-matrix for braiding (non-identical) particles around each other, and discuss the Hexagon equations which provide a consistency condition for the R-matrices. As with the pentagon, Hexagon solutions are also rigid.

•Sep 29, 2023•0 citations

Critical behavior and associated conformal algebra of the Z3 potts model

Vl.S. Dotsenko

Journal of Statistical Physics•Mar 1, 1984•55 citations

BRAIDS, LINK POLYNOMIALS AND TRANSFORMATIONS OF SOLVABLE MODELS

Tetsuo Deguchi

It is shown that braid matrices and link polynomials can be systematically constructed from exactly solvable models in statistical mechanics. Through symmetry breaking transformations, different braid matrices are derived from a solvable model. By associating the Markov traces with multi-variable representations, multi-variable link polynomials are obtained. Infinitesimal operators for braid matrices are constructed. Connection of our approach to the conformal field theories and the topological quantum field theory is discussed.

International Journal of Modern Physics A•Jun 10, 1990•6 citations

Braid matrices and structure constants for minimal conformal models

Giovanni Felder, J�rg Fr�hlich, G. Keller

Communications in Mathematical Physics•Dec 1, 1989•109 citations

Functional Equations and Fusion Matrices for the Eight Vertex Model

K. Fabricius, Barry M. McCoy

We derive sets of functional equations for the eight vertex model by exploiting an analogy with the functional equations of the chiral Potts model. From these equations we show that the fusion matrices have special reductions at certain roots of unity. We explicitly exhibit these reductions for the 3,4 and 5 order fusion matrices and compare our formulation with the algebra of Sklyanin.

arXiv:cond-mat/0311122•Nov 6, 2003•0 citations

Functional Equations and Fusion Matrices for the Eight Vertex Model

K. Fabricius, Barry M. McCoy

We derive sets of functional equations for the eight vertex model by exploiting an analogy with the functional equations of the chiral Potts model. From these equations we show that the fusion matrices have special reductions at certain roots of unity. We explicitly exhibit these reductions for the 3, 4 and 5 order fusion matrices and compare our formulation with the algebra of Sklyanin.

Publications of the Research Institute for Mathematical Sciences•Sep 30, 2004•35 citations
Investigating the transformation properties of the conformal blocks in the Z3{Z}_{3}Z3​ Potts model we derive some braid matrices. From the obtained braid matrices we explicitly show how the hexagon and pentagon identities are satisfied.
It is shown that braid matrices and link polynomials can be systematically constructed from exactly solvable models in statistical mechanics. Through symmetry breaking transformations, different braid matrices are derived from a solvable model. By associating the Markov traces with multi-variable representations, multi-variable link polynomials are obtained. Infinitesimal operators for braid matrices are constructed. Connection of our approach to the conformal field theories and the topological quantum field theory is discussed.