Macroscopic loops in the loop O(n) model

Tuesday, October 10, 2017 -
4:30pm to 5:30pm
A loop configuration on the hexagonal (honeycomb) lattice is a finite subgraph of the lattice in which every vertex has degree 0 or 2, so that every connected component is isomorphic to a cycle. The loop O(n) model on the hexagonal lattice is a random loop configuration, with the energy of of a loop configuration taken to be linear in the number of edges and the number of loops. I will discuss the resulting phase structure of the loop O(n) model, focusing on recent results about the non-existence of macroscopic loops for large n, and about the existence of macroscopic loops on a critical line when n is between 1 and 2. Talk based on joint works with Hugo Duminil-Copin, Alexander Glazman, Ron Peled and Wojciech Samotij.
Speaker: 
Yinon Spinka
Tel Aviv University
Event Location: 
Jadwin Hall 343