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

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.

38 pages, 11 figures

References in corpus (4)

• Inhomogeneous field theory inside the arctic circle
• The Influence of Boundary Conditions in the Six-Vertex Model
• Algebraic arctic curves in the domain-wall six-vertex model
• Generalized emptiness formation probability in the six-vertex model

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