The symmetric six-vertex model and the Segre cubic threefold

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.

12 pages

Cited by in corpus (2)

• Integrability and duality in spin chains
• Exactly Solved Models and Beyond: a special issue in honour of R J Baxter's 75th birthday