Philippe Di Francesco - Arctic curves for vertex models - IPAM at UCLA

May 21, 2024
Recorded 21 May 2024. Philippe Di Francesco of the University of Illinois at Urbana-Champaign presents "Arctic curves for vertex models" at IPAM's Vertex Models: Algebraic and Probabilistic Aspects of Universality Workshop. Abstract: 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. Learn more online at: