Macroscopic loops in the loop O(n) model
Macroscopic loops in the loop O(n) model

Yinon Spinka , Tel Aviv University
Jadwin Hall 343
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 nonexistence 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 DuminilCopin, Alexander Glazman, Ron Peled and Wojciech Samotij.