UVic Probability and Dynamics Seminar: Matan Harel

  • Date: 03/15/2022
  • Time: 14:30
Matan Harel, Northeastern



On the relation between delocalization of integer-valued height functions and the Berezinskii-Kosterlitz-Thouless phase transition


In this talk, we will discuss the relation between two types of two-dimensional lattice models: on one hand, we will consider the spin models with an O(2)-invariant interaction, such as the famous XY and Villain models. On the other, we study integer-valued height function models, where the interaction depends on the discrete gradient. We show that delocalization of a height function model implies that an associated O(2)-invariant spin model has a power-law decay phase. Motivated by this observation, we also extend the recent work of Lammers to show that a certain class of integer-valued height functions delocalize for all doubly periodic graphs (in particular, on the square lattice). Together, these results give a new perspective on the celebrated Berezinksii-Kosterlitz-Thouless phase transition for two-dimensional O(2)-invariant lattice models. This is joint work with Michael Aizenman, Ron Peled, and Jacob Shapiro.

Other Information: 

Time: 2:30pm - 3:30pm
Location: via Zoom


Please contact the aquas@uvic.ca for the Zoom link