An Elementary Proof of Phase Transition in the Planar XY Model

13.12.2021 16:15 – 18:15

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.

Lieu

Conseil Général 7-9, Salle 1-15, Séminaire "Mathématique physique"

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