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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 (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.
The Ising model on annealed complex networks with degree distribution decaying algebraically as $p(K)sim K^{-lambda}$ has a second-order phase transition at finite temperature if $lambda> 3$. In the absence of space dimensionality, $lambda$ controls
We explore a class of random tensor network models with ``stabilizer local tensors which we name Random Stabilizer Tensor Networks (RSTNs). For RSTNs defined on a two-dimensional square lattice, we perform extensive numerical studies of entanglement
We introduce a model for diffusion of two classes of particles ($A$ and $B$) with priority: where both species are present in the same site the motion of $A$s takes precedence over that of $B$s. This describes realistic situations in wireless and com
The zero-temperature Glauber dynamics is used to investigate the persistence probability $P(t)$ in the Potts model with $Q=3,4,5,7,9,12,24,64, 128$, $256, 512, 1024,4096,16384 $,..., $2^{30}$ states on {it directed} and {it undirected} Barabasi-Alber
Monte Carlo simulations are performed to study the two-dimensional Potts models with q=3 and 4 states on directed Small-World network. The disordered system is simulated applying the Heat bath Monte Carlo update algorithm. A first-order and second-or