Technion, IEM faculty - Seminar in Probability and Stochastic Processes
Speaker: Hugo Duminil-Copin
Title: Critical temperature of the square lattice Potts model
Date: 03/05/2011
Time: 11:30
Place: Hashmal-861
Abstract:  <>
In this talk, we derive the critical temperature of the q-state Potts model on the square
lattice (q  2). More precisely, we consider a geometric representation of the Potts model,
called the random-cluster model. Spin correlations of the Potts model get rephrased as
connectivity properties of the random-cluster model. The critical temperature of the
Potts model is therefore related to the critical point of the random-cluster model. For
the later, a duality relation allows us to compute the critical value using a crossing
estimate (similar to the celebrated Russo-Seymour-Welsh theory for percolation) and a
sharp threshold theorem. This result has many applications in the field and we will briefly
mention some of them at the end of the talk.
Joint work with V. Beffara.
Technion Math. Net (TECHMATH)
Editor: Michael Cwikel   <> 
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