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LA Probability Forum

Thursday, December 1, 2022
5:00pm to 6:00pm
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On delocalization of planar integer-valued height functions and the Berezinskii-Kosterlitz-Thouless phase transition of two-component spin models in two dimensions
Matan Harel, Department of Mathematics, Northeastern University,

Talk held at USC Kaprelian (KAP) 414

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 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 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.

For more information, please contact Math Dept by phone at 626-395-4335 or by email at [email protected].