Abstract:
The random-cluster model is a dependent percolation model where the weight of a configuration is proportional to q to the power of the number of connected components. It is highly related to the ferromagnetic q-Potts model, where every vertex is assigned one of q colors, and monochromatic neighbors are encouraged. Through non-rigorous means, Baxter showed that the phase transition is first-order whenever $q > 4$ - i.e. there are multiple Gibbs measures at criticality. In the first half of the talk, we show that this question is equivalent to a statement about six-vertex model. This is joint work with Hugo Duminil-Copin, Maxime Gangebin, Ioan Manolescu, and Vincent Tassion.
Biography:
Matan Harel is a Zuckerman STEM Leadership Postdoctoral Fellow at Tel Aviv University, supervised by Professor Ron Peled. Prior to that, he was a Postdoctoral Fellow at IHES Paris and the University of Geneva with Professor Hugo Duminil-Copin and Professor Stanislav Smirnov. He received his Ph.D. from the Courant Institute of Mathematical Sciences in New York.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai