Eigenvectors of Baxter-Bazhanov-Stroganov \tau^{(2)}(t_q) model with fixed-spin boundary conditions

The aim of this contribution is to give the explicit formulas for the eigenvectors of the transfer-matrix of Baxter-Bazhanov-Stroganov (BBS) model (N-state spin model) with fixed-spin boundary conditions. These formulas are obtained by a limiting procedure from the formulas for the eigenvectors of p...

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Bibliographic Details
Published inarXiv.org
Main Authors Iorgov, N Z, Shadura, V N, Tykhyy, Yu V
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 12.09.2007
Subjects
Boundary conditions
Eigenvectors
Ising model
Mathematical models
Mathematics - Mathematical Physics
Physics - Exactly Solvable and Integrable Systems
Physics - Mathematical Physics
Physics - Statistical Mechanics
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Summary:The aim of this contribution is to give the explicit formulas for the eigenvectors of the transfer-matrix of Baxter-Bazhanov-Stroganov (BBS) model (N-state spin model) with fixed-spin boundary conditions. These formulas are obtained by a limiting procedure from the formulas for the eigenvectors of periodic BBS model. The latter formulas were derived in the framework of the Sklyanin's method of separation of variables. In the case of fixed-spin boundaries the corresponding T-Q Baxter equations for the functions of separated variables are solved explicitly. As a particular case we obtain the eigenvectors of the Hamiltonian of Ising-like Z_N quantum chain model.
ISSN:2331-8422
DOI:10.48550/arxiv.0705.3236