Phase transition for the clock model via a generalized random cluster model

Nahuel Soprano Loto előadásának absztraktja

(Joint work with P. Ferrari and I. Armendáriz)

2013. szeptember 5. csütörtök, 16:15

 
 

The Edwards-Sokal coupling is a well known method that links the uniqueness of Gibbs measure in the Potts model with the lack of percolation under the associated random cluster measure. Comparing stochastically this random cluster measure with the Bernoulli bond percolation measure, it is possible to estimate the critical temperature of the Potts model. This coupling has also been used in other models such as the Ashkin-Teller model, the disordered ferromagnetic Potts model, the Edwards-Anderson spin-glass model and the Widom-Rowlinson model. These issues are developed in [1] and [2].
In this talk we show how to use this method to prove the positive correlation property for the q-state clock model and to find a temperature regime where there is lack of uniqueness of Gibbs measure.
This is a joint work with P. Ferrari and I. Armendáriz.
[1] Geoffrey Grimmett; The random-cluster model, volumen 333 de Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], Springer-Verlag, Berlin, 2006
[2] Georgii, Hans-Otto and Häggström, Olle and Maes, Christian;The random geometry of equilibrium phases, volumen 18 de Phase transitions and critical phenomena, Academic Press, San Diego, 2001.


 
Tóth Imre Péter, 2013.08.23