Arctic curves for vertex models

Philippe Di Francesco
University of Illinois at Urbana-Champaign

P. Di Francesco (University of Illinois at Urbana-Champaign and IPhT Paris Saclay)

Two-dimensional integrable lattice models that can be described in terms of (non-intersecting, possibly osculating)
paths with suitable boundary conditions display the arctic phenomenon: the emergence of a sharp phase boundary
between ordered cristalline phases (typically near the boundaries) and disordered liquid phases (away from them).
We show how the so-called tangent method can be applied to models such as the 6 Vertex model or its triangular
lattice variation the 20 Vertex model, to predict exact arctic curves. A number of companion combinatorial results
are obtained, relating these problems to tiling problems of associated domains of the plane.

Back to Workshop IV: Vertex Models: Algebraic and Probabilistic Aspects of Universality