Certain two-dimensional models in statistical mechanics have long been widely known or believed to exhibit arctic boundaries, which are sharp transitions from ordered (frozen) to disordered (temperate) phases. In this talk we will outline how to establish the existence, and explicitly determine, these arctic curves for the six-vertex model at ice point with domain-wall boundary data. The proof uses a probabilistic analysis of non-crossing directed path ensembles to provide a mathematical justification for the geometric tangent method, which is a general heuristic that was introduced by Colomo-Sportiello in 2016 for locating arctic boundaries of statistical mechanical models.
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