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SUMMARY:Critical temperature of the square lattice Potts model - Hugo Domi
 nil-Copin (Geneva)
DTSTART:20110315T163000Z
DTEND:20110315T173000Z
UID:TALK29291@talks.cam.ac.uk
CONTACT:Berestycki
DESCRIPTION:In this talk\, we derive the critical temperature of the q-sta
 te Potts model on the square\nlattice (q \\geq  2). More precisely\, we co
 nsider a geometric representation of the Potts model\,\ncalled the random-
 cluster model. Spin correlations of the Potts model get rephrased as\nconn
 ectivity properties of the random-cluster model. The critical temperature 
 of the\nPotts model is therefore related to the critical point of the rand
 om-cluster model. For\nthe later\, a duality relation allows us to compute
  the critical value using a crossing\nestimate (similar to the celebrated 
 Russo-Seymour-Welsh theory for percolation) and a\nsharp threshold theorem
 . This result has many applications in the eld and we will briefly\nmenti
 on some of them at the end of the talk. Joint work with V. Beara.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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