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arXiv · 1505.07418

The symmetric six-vertex model and the Segre cubic threefold

M. J. Martins
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Abstract

In this paper we investigate the mathematical properties of the integrability of the symmetric six-vertex model towards the view of Algebraic Geometry. We show that the algebraic variety originated from Baxter's commuting transfer method is birationally isomorphic to a ubiquitous threefold known as Segre cubic primal. This relation makes it possible to present the most generic solution for the Yang-Baxter triple associated to this lattice model. The respective $\mathrm{R}$-matrix and Lax operators are parametrized by three independent affine spectral variables.

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M. J. Martins. 2015-05-27. The symmetric six-vertex model and the Segre cubic threefold. https://doi.org/10.1088/1751-8113/48/33/334002

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