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Quantum geometry of 3-dimensional lattices
Vladimir V. Bazhanov, Vladimir V. Mangazeev, Sergey M. Sergeev
We study geometric consistency relations between angles on 3-dimensional (3D) circular quadrilateral lattices -- lattices whose faces are planar quadrilaterals inscribable into a c…
Faddeev-Volkov solution of the Yang-Baxter Equation and Discrete Conformal Symmetry
Vladimir V. Bazhanov, Vladimir V. Mangazeev, Sergey M. Sergeev
The Faddeev-Volkov solution of the star-triangle relation is connected with the modular double of the quantum group U_q(sl_2). It defines an Ising-type lattice model with positive…
Zamolodchikov's Tetrahedron Equation and Hidden Structure of Quantum Groups
Vladimir V. Bazhanov, Sergey M. Sergeev
The tetrahedron equation is a three-dimensional generalization of the Yang-Baxter equation. Its solutions define integrable three-dimensional lattice models of statistical mechanic…
Modified Tetrahedron Equations and Related 3D Integrable Models
H. E. Boos, V. V. Mangazeev, S. M. Sergeev
Using a modified version of the tetrahedron equations we construct a new family of -state three-dimensional integrable models with commuting two-layer transfer-matrices. We inve…