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

Simple item page
dc.creatorvon Gehlen, G.
dc.creatorPakuliak, S.
dc.creatorSergeev, S.
dc.date2003-05-20
dc.date2003-10-14
dc.date.accessioned2026-07-07T10:50:42Z
dc.date.available2026-07-07T10:50:42Z
dc.descriptionWe 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.
dc.description24 pages, 5 figures, typos corrected
dc.identifierhttps://arxiv.org/abs/nlin/0305031
dc.identifierhttp://arxiv.org/abs/nlin/0305031
dc.identifierJ.Phys.A37:1159-1179,2004
dc.identifierdoi:10.1088/0305-4470/37/4/005
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/184619
dc.subjectExactly Solvable and Integrable Systems
dc.subjectHigh Energy Physics - Theory
dc.titleTheta function parameterization and fusion for 3-D integrable Boltzmann weights
dc.typetext

Files

Collections

arXiv