The Bazhanov–Stroganov model from 3D approach

2005/05/31 by G. von Gehlen, G von Gehlen, S. Pakuliak +2 · 8 citations
Chemistry · Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic structures and combinatorial models #Discrete mathematics #Geometry #Graph #Integrable system #Isospectral #Mathematical physics #Mathematics #Molecular spectroscopy and chirality #Nonlinear Waves and Solitons #Operator (biology) #Parametrization (atmospheric modeling) #Physics #Pure mathematics #Quantum mechanics #Spin (aerodynamics) #Tetrahedron #Vertex (graph theory) #hep-th #nlin.SI

paper · pdf · doi:10.1088/0305-4470/38/33/005

published in Journal of Physics A Mathematical and General 38(33), 7269-7298 (Institute of Physics) · 33 pages, 6 figures

arxiv created 2005/07/15 · openalex publication_date 2005/08/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We apply a 3-dimensional approach to describe a new parametrization of the L-operators for the 2-dimensional Bazhanov-Stroganov (BS) integrable spin model related to the chiral Potts model. This parametrization is based on the solution of the associated classical discrete integrable system. Using a 3-dimensional vertex satisfying a modified tetrahedron equation, we construct an operator which generalizes the BS quantum intertwining matrix S. This operator describes the isospectral deformations of the integrable BS model.

Citations

• Theta-function parametrization and fusion for 3D integrable Boltzmann weights
• Explicit free parametrization of the modified tetrahedron equation
• The vertex formulation of the Bazhanov-Baxter model
• Quantum relativistic Toda chain at root of unity: isospectrality, modified Q-operator and functional Bethe ansatz
• Hidden Symmetries in the 6-Vertex Model of Statistical Physics