Speaker: Alex Karrila

Title:

On the delocalization of the six-vertex model

Abstract:

The six-vertex model is a planar random model, originally introduced as a toy model for the random crystalline structure of water ice. Today, it is interesting as an explicit connection of Conformal field theory and critical 2D random models, due to its natural representation as a random field, called the height function, and due to couplings to several other important random models (e.g., FK cluster model, Ising and Potts models, dimers, random graph homomorphisms).

I will discuss the different characterizations of localized/delocalized ("frozen"/"critical") phases of the model, our recent result identifying a critical parameter range, and its implications.

The talk is based on the preprint arXiv:2012.13750 with Hugo Duminil-Copin, Ioan Manolescu, and Mendes Oulamara.