Integrable quad equations derived from the quantum Yang-Baxter equation

DOI10.1007/s11005-020-01255-3zbMath1443.16041arXiv1803.03219OpenAlexW2793524934MaRDI QIDQ2190790

Andrew P. Kels

Publication date: 22 June 2020

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.03219

zbMATH Keywords

latticeconsistencyintegrablehypergeometricYang-BaxterABS

Mathematics Subject Classification ID

Exactly solvable models; Bethe ansatz (82B23) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Yang-Baxter equations (16T25) Partial difference equations (39A14)

Related Items (6)

Two-component Yang-Baxter maps and star-triangle relations ⋮ Gamma function solutions to the star-triangle equation ⋮ Lax matrices for lattice equations which satisfy consistency-around-a-face-centered-cube ⋮ Extended Z-invariance for integrable vector and face models and multi-component integrable quad equations ⋮ Interaction-round-a-face and consistency-around-a-face-centered-cube ⋮ Algebraic entropy for face-centered quad equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Quivers, YBE and 3-manifolds
• Discrete nonlinear hyperbolic equations. Classification of integrable cases
• Exact solution of the Faddeev-Volkov model
• Hyperbolic beta integrals
• On the Lagrangian structure of integrable quad-equations
• Limits of elliptic hypergeometric integrals
• The star-triangle relation, lens partition function, and hypergeometric sum/integrals
• Yang-Baxter maps, discrete integrable equations and quantum groups
• The modular properties and the integral representations of the multiple elliptic gamma functions
• Classification of integrable equations on quad-graphs. The consistency approach
• The discrete Korteweg-de Vries equation
• A master solution of the quantum Yang-Baxter equation and classical discrete integrable equations
• A generalized hypergeometric function satisfying four analytic difference equations of Askey-Wilson type
• Faddeev-Volkov solution of the Yang-Baxter equation and discrete conformal symmetry
• Tensor product spaces
• Partition function of the eight-vertex lattice model
• A generalized hypergeometric function. III: Associated Hilbert space transform
• The discrete and continuous Painlevé VI hierarchy and the Garnier systems
• On the elliptic beta function
• Nonlinear Partial Difference Equations. I. A Difference Analogue of the Korteweg-de Vries Equation
• Elliptic beta integrals and solvable models of statistical mechanics
• Elliptic N-soliton Solutions of ABS Lattice Equations
• Quasi-classical expansion of the star-triangle relation and integrable systems on quad-graphs
• New solutions of the star–triangle relation with discrete and continuous spin variables
• Lagrangian multiforms and multidimensional consistency
• Some Hypergeometric Orthogonal Polynomials
• QUANTUM DILOGARITHM
• First order analytic difference equations and integrable quantum systems
• Bäcklund transformation for the Krichever-Novikov equation
• Exactly solved models on planar graphs with vertices in $\mathbb{Z}^3$
• Lens elliptic gamma function solution of the Yang–Baxter equation at roots of unity
• On the Lagrangian structure of 3D consistent systems of asymmetric quad-equations

This page was built for publication: Integrable quad equations derived from the quantum Yang-Baxter equation