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:  <http://ie.technion.ac.il/seminar_files/1302678118_Technion2011.pdf>
 
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.
 
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