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CATEGORIES:Probability
SUMMARY:Discontinuity of the phase transition for the plan
ar random-cluster and Potts models with q >\; 4
- Matan Harel (IHES Paris)
DTSTART;TZID=Europe/London:20161025T163000
DTEND;TZID=Europe/London:20161025T173000
UID:TALK67744AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/67744
DESCRIPTION:The ferromagnetic q-Potts Model is a classical spi
n system in which one of q colors is placed at eve
ry vertex of a graph and assigned an energy propor
tional to the number of monochromatic neighbors. I
t is highly related to the Random Cluster model\,
which is a dependent percolation model where a con
figuration is weighted by q to the power of the nu
mber of clusters. Through non-rigorous means\, Bax
ter showed that the phase transition is first-orde
r whenever q > 4 - i.e. there exists multiple Gibb
s states at criticality. We provide a rigorous pro
of of the second claim. Like Baxter\, our proof us
es the correspondence between the above models and
the Six-Vertex model\, which we analyze using the
Bethe ansatz and transfer matrix techniques. We a
lso prove Baxter's formula for the correlation len
gth of the models at criticality. This is joint wo
rk with Hugo Duminil-Copin\, Maxemine Gangebin\, I
oan Manolescu\, and Vincent Tassion.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0W
B
CONTACT:Perla Sousi
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