The Influence of Boundary Conditions in the Six-Vertex Model

TL;DR

This paper investigates how different boundary conditions affect the continuum limit of the six-vertex model, deriving a variational principle and explicit PDEs in certain cases, enhancing understanding of phase behavior.

Contribution

It introduces a variational principle for the height function with arbitrary boundary conditions and computes explicit PDEs using Bethe Ansatz in specific scenarios.

Findings

Boundary conditions significantly influence the continuum limit.

Explicit PDEs are derived for particular boundary cases.

The phase diagram's implications are discussed in this context.

Abstract

We discuss the influence of boundary conditions on the continuum limit of the six-vertex model by deriving a variational principle for the associated height function with arbitrary fixed boundary conditions. We discuss its consequences using the known phase diagram of the six-vertex model. In some particular cases we compute explicitly the corresponding partial differential equations by means of the Bethe Ansatz.