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Marcin Lis, University of Vienna, Austria
April 13, 2022 @ 6:00 pm - 7:00 pm UTC+4
Title: “An elementary proof of phase transition in the planar XY model”.
Abstract: Using elementary methods we obtain a power-law lower bound on the two-point function of the planar XY spin model at low temperatures. This was famously first rigorously obtained by Fröhlich and Spencer and establishes a Berezinskii-Kosterlitz-Thouless phase transition in the model. Our argument relies on a new loop representation of spin correlations, a recent result of Lammers on delocalisation of integer-valued height functions, and classical correlation inequalities. This is joint work with Diederik van Engelenburg.