Séminaire de groupe
|Critical behaviour of the Potts model on complex networks|
|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 man-made 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 node-degree distribution manifests a power-law decay governed by the exponent $\lambda$. We work within the mean-led approximation, since for systems on random uncorrelated scale-free networks (where the very notion of a space dimension is ill-dened) this method is known often to give asymptotically exact results. Depending on particular values of $q$ and one observes either the 1st-order or the second-order 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 scale-free network. Interestingly, logarithmic corrections to scaling appear at $\lambda = 4$ in this case.