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SUMMARY:Discontinuity of the phase transition for the planar random-cluste
 r and Potts models with q &gt\; 4 - Matan Harel (IHES Paris)
DTSTART:20161025T153000Z
DTEND:20161025T163000Z
UID:TALK67744@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION:The ferromagnetic q-Potts Model is a classical spin system in 
 which one of q colors is placed at every vertex of a graph and assigned an
  energy proportional to the number of monochromatic neighbors. It is highl
 y related to the Random Cluster model\, which is a dependent percolation m
 odel where a configuration is weighted by q to the power of the number of 
 clusters. Through non-rigorous means\, Baxter showed that the phase transi
 tion is first-order whenever q > 4 - i.e. there exists multiple Gibbs stat
 es at criticality. We provide a rigorous proof of the second claim. Like B
 axter\, our proof uses the correspondence between the above models and the
  Six-Vertex model\, which we analyze using the Bethe ansatz and transfer m
 atrix techniques. We also prove Baxter's formula for the correlation lengt
 h of the models at criticality. This is joint work with Hugo Duminil-Copin
 \, Maxemine Gangebin\, Ioan Manolescu\, and Vincent Tassion.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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