Geodesic
Spectral Curves and Parameterization of a Discrete Integrable Three-Dimensional Model
Teoretičeskaâ i matematičeskaâ fizika, Tome 136 (2003) no. 1, pp. 30-51

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We consider a discrete classical integrable model on a three-dimensional cubic lattice. The solutions of this model can be used to parameterize the Boltzmann weights of various three-dimensional spin models. We find the general solution of this model constructed in terms of the theta functions defined on an arbitrary compact algebraic curve. Imposing periodic boundary conditions fixes the algebraic curve. We show that the curve then coincides with the spectral curve of the auxiliary linear problem. For a rational curve, we construct the soliton solution of the model.
Keywords: three-dimensional integrable systems, Bäcklund transformations, spectral curves. 
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S. Z. Pakulyak; S. M. Sergeev. Spectral Curves and Parameterization of a Discrete Integrable Three-Dimensional Model. Teoretičeskaâ i matematičeskaâ fizika, Tome 136 (2003) no. 1, pp. 30-51. http://geodesic.mathdoc.fr/item/TMF_2003_136_1_a2/