Work

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

Year: 2004

Type: article

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.

Source: Journal of Physics A Mathematical and General

DOI: 10.1088/0305-4470/37/4/005

Authors: G von Gehlen, S Pakuliak, S Sergeev

Institutions: University of Bonn, Joint Institute for Nuclear Research, Australian National University, Max Planck Institute for Mathematics

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Russian Foundation for Basic Research

Awards: G4975180307, G8612426124