Published 09/07/2018
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Phase transitions in the potts model on complex networks

B.Berche , M.Krasnytska , Y.Holovatch

Here, we will analyze the impact of changes in the topology of the underlying structure on ther-modynamics of this model, when Potts spins reside on the nodes of an uncorrelated scale-free network, as explained more in detail below. Smoothing of the rst order phase transition for the Potts model with large values of q on scale-free evolving networks was observed in. In this paper, we will calculate thermodynamic functions of the Potts model on an uncorrelated scale-free network.
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 lambda. 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 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 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.
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