## Phase transitions in the Potts model on complex networks    [PDF]

M. Krasnytska, B. Berche, Yu. Holovatch
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. We consider the q-state Potts model on an uncorrelated scale-free network for which the node-degree distribution manifests a power-law decay governed by the exponent \lambda. We work within the mean-field approximation, since for systems on random uncorrelated scale-free networks this method is known often to give asymptotically exact results. Depending on particular values of q and \lambda one observes either a first-order or a second-order phase transition or the system is ordered at any finite temperature. In a case study, we consider the limit q=1 (percolation) and find 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.
View original: http://arxiv.org/abs/1302.3386