Critical temperature of the square lattice Potts model
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In this talk, we derive the critical temperature of the qstate Potts model on the square
lattice (q \geq 2). More precisely, we consider a geometric representation of the Potts model,
called the randomcluster model. Spin correlations of the Potts model get rephrased as
connectivity properties of the randomcluster model. The critical temperature of the
Potts model is therefore related to the critical point of the randomcluster model. For
the later, a duality relation allows us to compute the critical value using a crossing
estimate (similar to the celebrated RussoSeymourWelsh theory for percolation) and a
sharp threshold theorem. This result has many applications in the eld and we will briefly
mention some of them at the end of the talk. Joint work with V. Beara.
This talk is part of the Probability series.
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