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University of Cambridge > Talks.cam > Probability > Discontinuity of the phase transition for the planar random-cluster and Potts models with q > 4

## Discontinuity of the phase transition for the planar random-cluster and Potts models with q > 4Add to your list(s) Download to your calendar using vCal - Matan Harel (IHES Paris)
- Tuesday 25 October 2016, 16:30-17:30
- MR12, CMS, Wilberforce Road, Cambridge, CB3 0WB.
If you have a question about this talk, please contact Perla Sousi. 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 highly related to the Random Cluster model, which is a dependent percolation model where a configuration is weighted by q to the power of the number of clusters. Through non-rigorous means, Baxter showed that the phase transition is first-order whenever q > 4 – i.e. there exists multiple Gibbs states at criticality. We provide a rigorous proof of the second claim. Like Baxter, our proof uses the correspondence between the above models and the Six-Vertex model, which we analyze using the Bethe ansatz and transfer matrix techniques. We also prove Baxter’s formula for the correlation length of the models at criticality. This is joint work with Hugo Duminil-Copin, Maxemine Gangebin, Ioan Manolescu, and Vincent Tassion. This talk is part of the Probability series. ## This talk is included in these lists:- All CMS events
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