香蕉视频

Title: Delocalization of integer-valued height functions and the Berezinskii-Kosterlitz-Thouless phase transition for O(2)-invariant spin models

Abstract: In this talk, we will discuss the relationship between two types of two-dimensional lattice models: on the one hand, we will consider 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 the delocalization of a height function model implies that an associated O(2)-invariant spin model decay phase. Motivated by this, we also extend the recent work of Lammers to show that a certain class of integer-valued height functions undergo a roughening phase transition for all doubly periodic planar graphs (in particular, on the square lattice). Together, these results give a new perspective on the Berezinskii-Kosterlitz-Thouless phase transition for two-dimensional O(2)-invariant lattice models.
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This is joint work with Michael Aizenman, Ron Peled, and Jacob Shapiro.