Martins, M. J. The symmetric six-vertex model and the Segre cubic threefold. (English) Zbl 1329.82030 J. Phys. A, Math. Theor. 48, No. 33, Article ID 334002, 9 p. (2015). Summary: 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 \(R\)-matrix and Lax operators are parameterized by three independent affine spectral variables. Cited in 1 Document MSC: 82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics 37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) Keywords:integrable models; six-vertex model; Segre threefold PDFBibTeX XMLCite \textit{M. J. Martins}, J. Phys. A, Math. Theor. 48, No. 33, Article ID 334002, 9 p. (2015; Zbl 1329.82030) Full Text: DOI arXiv