Mathematical Physics and Harmonic Analysis Seminar

Date: December 8, 2021

Time: 10:00AM - 11:00AM

Location: BLOC 628

Speaker: Jacob Shapiro, Princeton

Title: Delocalization in the integer-valued Gaussian Field and the BKT phase of the 2D Villain model

Abstract: It is shown that the Villain model of two-component spins over two dimensional lattices exhibits slow, non-summable, decay of correlations at any temperature at which the dual integer-valued Gaussian field exhibits delocalization. For the latter, we extend the recent proof by Lammers of a delocalization transition in two dimensional graphs of degree three, to all doubly periodic graphs, in particular to Z^2. Taken together these two statements yield a new perspective on the BKT phase transition in the Villain model, and a new proof on delocalization in two dimensional integer-valued height functions. Joint with Aizenman, Harel and Peled.