Abstract:
The six-vertex model is a widely-studied lattice model whose configuration space is orientations of the edges of the square lattice in which every vertex has in-degree of exactly 2. Each of the six possible vertex configuration is assigned a weight (subject to some symmetry conditions), and the entire configuration is weighted multiplicatively. In the late 1960's, Lieb showed that the Bethe ansatz, first developed to study the one-dimensional quantum Heisenberg chain, can be used without modification to study the six-vertex transfer matrix. Follow up work by Lieb, Yang and Yang, and Baxter used non-rigorous methods to explicitly compute several macroscopic quantities associated with the model. We provide a rigorous proof for Lieb and Baxter's formulas for free-energy and spectral-theoretic correlation length when c >2. This also implies the discontinuity of the phase transition for the random-cluster and Potts models with q>4. 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