Arctic curves of the 20V model on a triangle

TL;DR

This paper uses the Tangent Method to predict arctic curves in the 20V model on a triangle, revealing a complex phase diagram with frozen and liquid phases, and connects it to the Six Vertex model through integrability.

Contribution

It introduces a novel application of the Tangent Method to the 20V model on a triangular domain, expanding understanding of phase boundaries in integrable models.

Findings

Identified six frozen phases and one liquid phase in the phase diagram.

Derived arctic curves using the Tangent Method.

Performed exact enumeration of configurations.

Abstract

We apply the Tangent Method of Colomo and Sportiello to predict the arctic curves of the Twenty Vertex model with specific domain wall boundary conditions on a triangle, in the Disordered phase, leading to a phase diagram with six types of frozen phases and one liquid one. The result relies on a relation to the Six Vertex model with domain wall boundary conditions and suitable weights, as a consequence of integrability. We also perform the exact refined enumeration of configurations.