Arctic curves of the six-vertex model on generic domains: the Tangent Method

TL;DR

This paper introduces the Tangent Method for deriving Arctic curves in the six-vertex model, extending its applicability to various domains and models with limit shape phenomena, including a triangoloid domain at the ice-point.

Contribution

The paper presents an alternative, adaptable method for determining Arctic curves, previously only conjectured, in the six-vertex model across diverse domains and models.

Findings

Recovered the conjectured Arctic curve in the square domain.

Derived the Arctic curve for a triangoloid domain at the ice-point.

Extended the method to a broad class of domains and models.

Abstract

We revisit the problem of determining the Arctic curve in the six-vertex model with domain wall boundary conditions. We describe an alternative method, by which we recover the previously conjectured analytic expression in the square domain. We adapt the method to work for a large class of domains, and for other models exhibiting limit shape phenomena. We study in detail some examples, and derive, in particular, the Arctic curve of the six-vertex model in a triangoloid domain at the ice-point.