Spectral curves and parameterizations of a discrete integrable 3-dimensional model

2002/09/09 by S. Pakuliak, Pakuliak, S., С. М. Сергеев +2 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Advanced Differential Geometry Research #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Waves and Solitons #nlin.SI

paper · pdf · doi:10.48550/arxiv.nlin/0209019

22 pages, 6 figures

arxiv created 2002/09/09 · openalex publication_date 2002/09/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a discrete classical integrable model on the 3-dimensional cubic lattice. The solutions of this model can be used to parameterize the Boltzmann weights of the different 3-dimensional spin models. We have found the general solution of this model constructed in terms of the theta-functions defined on an arbitrary compact algebraic curve. The imposing of the periodic boundary conditions fixes the algebraic curve. We have shown that in this case the curve coincides with the spectral one of the auxiliary linear problem. In the case when the curve is a rational one, the soliton solutions have been constructed.

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

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