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SUMMARY:A topological transition in the XY model - Diederik van Engelenbur
 g (Lyon)
DTSTART:20231114T140000Z
DTEND:20231114T150000Z
UID:TALK208528@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION:In contrast to spin system taking value in a finite group\, th
 ose invariant under the action of the rotation group SO(2) never have an o
 rdered phase in if the lattice is 2-dimensional.  So what does happen? In 
 the sixties\, physicist Berezinskii\, Kosterlitz and Thouless predicted th
 at 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 c
 alled the BKT transition. In the late eighties Fröhlich and Spencer famou
 sly 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 whic
 h allows to transfer information between the model itself and its dual hei
 ght function. I will use the link to give a new proof of the BKT transitio
 n. The loop representation can also be used to provide simple proofs of co
 rrelation inequalities. Based on joint work with Marcin Lis.
LOCATION:MR12
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