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. --------------------------------------------------------- Technion Math. Net (TECHMATH) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: <rami@.technion.ac.il>