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## A topological transition in the XY modelAdd to your list(s) Download to your calendar using vCal - Diederik van Engelenburg (Lyon)
- Tuesday 14 November 2023, 14:00-15:00
- MR12.
If you have a question about this talk, please contact Perla Sousi. In contrast to spin system taking value in a finite group, those invariant under the action of the rotation group SO(2) never have an ordered phase in if the lattice is 2-dimensional. So what does happen? In the sixties, physicist Berezinskii, Kosterlitz and Thouless predicted that a more subtle phase transition should appear if the spins are abelian; in terms of the two-point functions this manifests itself as a transition between exponential decay and power-law behavior. The transition is now called the BKT transition. In the late eighties FrÃ¶hlich and Spencer famously provided a rigorous proof of such a transition in the planar XY model. In the talk, I will introduce a loop representation of the XY model which allows to transfer information between the model itself and its dual height function. I will use the link to give a new proof of the BKT transition. The loop representation can also be used to provide simple proofs of correlation inequalities. Based on joint work with Marcin Lis. This talk is part of the Probability series. ## This talk is included in these lists:- All CMS events
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