Phase transitions in the Potts model on complex networks

Abstract

The Potts model is one of the most popular spin models of statistical physics. The prevailing majority of 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 λ. We work within the mean-field approximation, since for systems on random uncorrelated scale-free networks this method is known to often give asymptotically exact results. Depending on particular values of q and λone 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 λ=4 in this case.

15 pages, 2 figures

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• Generalized Ising Model on a Scale-Free Network: An Interplay of Power Laws
• Potts Model with Invisible States: A Review
• Ising model with variable spin/agent strengths
• Ising model with invisible states on scale-free networks
• Collective decision-making with heterogeneous biases: Role of network topology and susceptibility
• Scaling functions and amplitude ratios for the Potts model on an uncorrelated scale-free network