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LA Probability Forum

Thursday, March 10, 2022
4:00pm to 5:00pm
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An elementary proof of phase transition in the planar XY model
Diederik van Engelenburg, Vienna School of Mathematics, University of Vienna,

Will be held at UCLA - talks in Math Sciences Room 6627

We derive, with elementary methods, a power-law bound on the two-point function of the planar XY model at low temperatures and therefore show the model undergoes a Berezinskii-Kosterlitz-Thouless phase transition. This was famously first rigorously proved by Fröhlich and Spencer in the eighties. Our argument relies on a new loop representation of spin correlations and a recent result by Lammers on the delocalisation of integer-valued height functions. The main contribution is a switching lemma for the loop representation that can also be used to prove some classical correlation inequalities. Joint work with Marcin Lis.

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