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

Gunter Von Gehlen, Stanislav Pakuliak, S. Sergeev

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

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
Volume37
Issue number4
DOIs
Publication statusPublished - 30 Jan 2004
Externally publishedYes

Fingerprint

Triangular pyramid
Theta Functions
Ludwig Boltzmann
Parametrization
tetrahedrons
Fusion
Fusion reactions
fusion
nth root
Fermat
Spin Models
Algebraic curve
Lattice Model
Periodic Boundary Conditions
Partition Function
Equations of motion
boxes
partitions
Equations of Motion
equations of motion

Cite this

Von Gehlen, Gunter ; Pakuliak, Stanislav ; Sergeev, S. / Theta-function parametrization and fusion for 3D integrable Boltzmann weights. In: Journal of Physics A: Mathematical and General. 2004 ; Vol. 37, No. 4. pp. 1159-1179.
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Theta-function parametrization and fusion for 3D integrable Boltzmann weights. / Von Gehlen, Gunter; Pakuliak, Stanislav; Sergeev, S.

In: Journal of Physics A: Mathematical and General, Vol. 37, No. 4, 30.01.2004, p. 1159-1179.

Research output: Contribution to journalArticle

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