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Theta function parameterization and fusion for 3-D integrable Boltzmann weights

G. von Gehlen·S. Pakuliak·S. Sergeev
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Abstract

We report progress in constructing Boltzmann weights for integrable 3-dimensional lattice spin models. We show that a large class of vertex solutions to the modified tetrahedron equation can be conveniently parameterized in terms of N-th roots of theta-functions on the Jacobian of a compact algebraic curve. Fay's identity guarantees the Fermat relations and the classical equations of motion for the parameters determining the Boltzmann weights. Our parameterization allows to write a simple formula for fused Boltzmann weights R which describe the partition function of an arbitrary open box and which also obey the modified tetrahedron equation. Imposing periodic boundary conditions we observe that the R satisfy the normal tetrahedron equation. The scheme described contains the Zamolodchikov-Baxter-Bazhanov model and the Chessboard model as special cases.

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G. von Gehlen, S. Pakuliak, S. Sergeev. 2003-10-14. Theta function parameterization and fusion for 3-D integrable Boltzmann weights. https://doi.org/10.1088/0305-4470%2F37%2F4%2F005

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