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

Gunter Von Gehlen, Stanislav Pakuliak, S. Sergeev

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


We report progress in constructing Boltzmann weights for integrable three-dimensional lattice spin models. We show that a large class of vertex solutions to the modified tetrahedron equation (MTE) can be conveniently parametrized in terms of Nth 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 parametrization allows us to write a simple formula for fused Boltzmann weights fractur R sign 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 fractur R sign satisfy the normal tetrahedron equation. The scheme described contains the Zamolodchikov-Baxter-Bazhanov model and the chessboard model as special cases.

Original languageEnglish
Pages (from-to)1159-1179
Number of pages21
JournalJournal of Physics A: Mathematical and General
Issue number4
Publication statusPublished - 30 Jan 2004
Externally publishedYes


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