The Baxter–Bazhanov–Stroganov model: separation of variables and the Baxter equation

2006/03/12 by G. von Gehlen, G von Gehlen, N. Iorgov +5 · 3 citations
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #cond-mat.stat-mech #math-ph #math.MP #nlin.SI

paper · pdf · doi:10.1088/0305-4470/39/23/006

published as J. Phys. A: Math. Gen. 39 (2006) 7257-7282 · 28 pages

arxiv created 2006/03/12 · openalex publication_date 2006/05/23 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

The Baxter-Bazhanov-Stroganov model (also known as the τ^(2) model) has attracted much interest because it provides a tool for solving the integrable chiral Z_N-Potts model. It can be formulated as a face spin model or via cyclic L-operators. Using the latter formulation and the Sklyanin-Kharchev-Lebedev approach, we give the explicit derivation of the eigenvectors of the component B_n(λ) of the monodromy matrix for the fully inhomogeneous chain of finite length. For the periodic chain we obtain the Baxter T-Q-equations via separation of variables. The functional relations for the transfer matrices of the τ^(2) model guarantee non-trivial solutions to the Baxter equations. For the N=2 case, which is free fermion point of a generalized Ising model, the Baxter equations are solved explicitly.

Citations

• Superintegrable chiral Potts model: Thermodynamic properties, an ?inverse? model, and a simple associated Hamiltonian

Cited by

• Form-factors in the Baxter–Bazhanov–Stroganov model II: Ising model on the finite lattice
• Reconstruction of Baxter Q-operator from Sklyanin SOV for cyclic representations of integrable quantum models
• On theτ(2)-model in the chiral Potts model and cyclic representation of the quantum groupUq(sl2)