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

2016/05/04 by Filippo Colomo, Andrea Sportiello · 2 citations
Mathematics · Physics and Astronomy · #cond-mat.stat-mech #math-ph #math.CO #math.MP

paper · pdf · doi:10.1007/s10955-016-1590-0

published as J. Stat. Phys. 164 (2016) 1488 · 38 pages, 11 figures

arxiv created 2016/05/04 · arxiv updated 2016/11/07

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.

Cited by

• Concavity analysis of the tangent method
• Two dimensional inhomogeneous classical systems at criticality
• The asymmetric five vertex model on a rectangle

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