Integrability of Limit Shapes of the Inhomogeneous Six Vertex Model

TL;DR

This paper proves that the limit shape equations for the inhomogeneous six vertex model possess infinitely many conserved quantities, indicating integrability of the model's limit shape equations.

Contribution

It establishes the integrability of the limit shape equations for the inhomogeneous six vertex model by demonstrating the existence of infinitely many conserved quantities.

Findings

Euler-Lagrange equations have infinitely many conserved quantities

Limit shape equations are integrable

Advances understanding of inhomogeneous six vertex model

Abstract

In this paper we prove that the Euler-Lagrange equations for the limit shape for the inhomogeneous six vertex model on a cylinder have infinitely many conserved quantities.