Cylinder partition function of the 6-vertex model from algebraic geometry

Zoltan Bajnok , Jesper Lykke Jacobsen (1, 2) , Yunfeng Jiang , Rafael I. Nepomechie , Yang Zhang

1 IPHT - Institut de Physique Théorique - UMR CNRS 3681
2 Champs Aléatoires et Systèmes hors d'Équilibre

We compute the exact partition function of the isotropic 6-vertex model on a cylinder geometry with free boundary conditions, for lattices of intermediate size, using Bethe ansatz and algebraic geometry. We perform the computations in both the open and closed channels. We also consider the partial thermodynamic limits, whereby in the open (closed) channel, the open (closed) direction is kept small while the other direction becomes large. We compute the zeros of the partition function in the two partial thermodynamic limits, and compare with the condensation curves.

Mots clés: Bethe Ansatz; Differential and Algebraic Geometry; Lattice Integrable Models; model: vertex; partition function; algebraic geometry; thermodynamical; cylinder; boundary condition; Bethe ansatz; condensation; geometry; lattice

Domaines: Physique des Hautes Energies - Théorie [hep-th]; Physique Générale [physics.gen-ph]

Zoltan Bajnok, Jesper Lykke Jacobsen, Yunfeng Jiang, Rafael I. Nepomechie, Yang Zhang. Cylinder partition function of the 6-vertex model from algebraic geometry. Journal of High Energy Physics, 2020, 06, pp.169. ⟨10.1007/JHEP06(2020)169⟩. ⟨hal-02504618⟩