The Many Faces of the Chiral Potts Model

Abstract

In this talk, we give a brief overview of several aspects of the theory of the chiral Potts model, including higher-genus solutions of the star-triangle and tetrahedron equations, cyclic representations of affine quantum groups, basic hypergeometric functions at root of unity, and possible applications.

16 pages, LaTeX 2.09 or 2E, 8 eps figures, uses psfig.tex

Cited by in corpus (20)

• Parafermionic edge zero modes in Z_n-invariant spin chains
• Topological phases with parafermions: theory and blueprints
• Free parafermions
• Numerical study of the chiral ${\mathbb{Z}}_3$ quantum phase transition in one spatial dimension
• Zamolodchikov's Tetrahedron Equation and Hidden Structure of Quantum Groups
• Quantum field theory for the chiral clock transition in one spatial dimension
• Parafermionic conformal field theory on the lattice
• Parafermionic phases with symmetry-breaking and topological order
• Onsager symmetries in $U(1)$-invariant clock models
• Parafermionic clock models and quantum resonance
• Non-diagonal anisotropic quantum Hall states
• The Large N Limits of the Chiral Potts Model
• Onsager's algebra and partially orthogonal polynomials
• Identifying the Huse-Fisher universality class of the three-state chiral Potts model
• The grand canonical ABC model: a reflection asymmetric mean field Potts model
• Bazhanov-Stroganov model from 3D approach
• Integrable Hamiltonians with $D(D_n)$ symmetry from the Fateev-Zamolodchikov model
• The Yang-Baxter integrability of the critical Ising chain
• A Graph-Theoretic Framework for Free-Parafermion Solvability
• About 30 Years of Integrable Chiral Potts Model, Quantum Groups at Roots of Unity and Cyclic Hypergeometric Functions