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Vertex Models and Knot invariants

P. Ramadevi

Texts and readings in physical sciencesJan 1, 20170 citations

SPATIAL SYMMETRY, LOCAL INTEGRABILITY AND TETRAHEDRON EQUATIONS IN THE BAXTER-BAZHANOV MODEL

Rinat Kashaev, Vladimir V. Mangazeev, Yu. G. Stroganov

We show that the Baxter-Bazhanov model is invariant under the action of the cube’s symmetry group. The three-dimensional star-star relations, proposed by Baxter and Bazhanov as local integrability conditions, correspond to a particular transformation from this group. Invariant Boltzmann weights, parametrized in terms of the Zamolodchikov angle variables, apparently satisfy the tetrahedron equations.

International Journal of Modern Physics AJan 30, 199332 citations

Exactly solvable models and knot theory

Miki Wadati, Tetsuo Deguchi, Yasuhiro Akutsu

Physics ReportsSep 1, 1989281 citations

The Lax pair for the fermionic Bazhanov-Stroganov R-operator

A. Melikyan, G. Weber

We derive the Lax connection of the free fermion model on a lattice starting from the fermionic formulation of Bazhanov-Stroganov's three-parameter elliptic parametrization for the R-operator. It results in the Yang-Baxter and decorated Yang-Baxter equations of difference type in one of the spectral parameters, which is the most suitable form to obtain any relativistic model of free fermions in the continuous limit.

arXiv:2011.03066Physics Letters BDec 8, 20205 citations

Eigenvectors of Baxter–Bazhanov–Stroganov τ (2) (tq) model with fixed-spin boundary conditions

N. Z. Iorgov, V. N. Shadura, Yu Tykhyy

We give explicit formulas for the eigenvectors of the transfer matrix of the Baxter-Bazhanov-Stroganov (BBS) model (N-state spin model) with fixed-spin boundary conditions. We obtain these formulas from the formulas for the eigenvectors of the periodic BBS model by a limit procedure. The latter formulas were derived in the framework of Sklyanin’s method of separation of variables. In the case of fixed-spin boundaries, we solve the corresponding T-Q Baxter equations for the functions of separated variables explicitly. As a particular case, we obtain the eigenvectors of the Hamiltonian of the Ising-like ℤN quantum chain model.We give explicit formulas for the eigenvectors of the transfer matrix of the Baxter-Bazhanov-Stroganov (BBS) model (N-state spin model) with fixed-spin boundary conditions. We obtain these formulas from the formulas for the eigenvectors of the periodic BBS model by a limit procedure. The latter formulas were derived in the framework of Sklyanin’s method of separation of variables. In the case of fixed-spin boundaries, we solve the corresponding T-Q Baxter equations for the functions of separated variables explicitly. As a particular case, we obtain the eigenvectors of the Hamiltonian of the Ising-like ℤN quantum chain model.

Nov 21, 20122 citations

Quantum knots and knotted zeros: part II (Conference Presentation)

Samuel J. Lomonaco, Louis Hirsch Kauffman

May 14, 20190 citations

Knot invariants associated with a particularN→∞ continuous limit of the Baxter-Bazhanov model

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