Finite-size scaling and the toroidal partition function of the critical asymmetric six-vertex model

TL;DR

This paper analyzes finite-size effects in the critical asymmetric six-vertex model using Bethe ansatz, relating anisotropy and susceptibilities, and derives a modular covariant toroidal partition function considering incommensurability and boundary conditions.

Contribution

It provides a novel derivation of the toroidal partition function incorporating incommensurability and boundary effects in the critical asymmetric six-vertex model.

Findings

Finite-size corrections linked to bulk susceptibilities.

Universal Gaussian coupling constant expressed via Hessian of free energy.

Derived modular covariant toroidal partition function with incommensurability effects.

Abstract

Finite-size corrections to the energy levels of the asymmetric six-vertex model transfer matrix are considered using the Bethe ansatz solution for the critical region. The non-universal complex anisotropy factor is related to the bulk susceptibilities. The universal Gaussian coupling constant $g$ is also related to the bulk susceptibilities as $g=2H^{-1/2}/\pi$, $H$ being the Hessian of the bulk free energy surface viewed as a function of the two fields. The modular covariant toroidal partition function is derived in the form of the modified Coulombic partition function which embodies the effect of incommensurability through two mismatch parameters. The effect of twisted boundary conditions is also considered.