Séminaire de groupe
Critical behaviour of the Potts model on complex networks 
Mariana Krasnytska 
ICMP Lviv 
jeudi 31 janvier 2013 , 10h25 
Salle de séminaire du groupe de Physique Statistique 
The Potts model is one of the most popular spin models of statistical physics. Prevailing majority of the work done so far corresponds to the lattice version of the model. However, many natural or manmade systems are much better described by the topology of a network or a random graph. We consider the $q$state Potts model on a complex network for which the nodedegree distribution manifests a powerlaw decay governed by the exponent $\lambda$. We work within the meanled approximation, since for systems on random uncorrelated scalefree networks (where the very notion of a space dimension is illdened) this method is known often to give asymptotically exact results. Depending on particular values of $q$ and one observes either the 1storder or the secondorder phase transition or the system is ordered at any temperature. In a case study, we consider the limit $q \to 1$ (percolation) and 2nd a correspondence between the magnetic exponents and those describing percolation on a scalefree network. Interestingly, logarithmic corrections to scaling appear at $\lambda = 4$ in this case. 
