Potts Model with q States on Directed Barabási-Albert Networks (Communications in Computational Physics, 2007)
On directed Barabási-Albert networks with two and seven neighbours selected by each added site, the Ising model with spin S = 1/2 was seen not to show aspontaneous magnetisation. Instead, the decay time for flipping of the magnetisationfollowed an Arrhenius law for Metropolis and Glauber algorithms, but for Wolff cluster flipping the magnetisation decayed exponentially with time. However, on thesenetworks the Ising model spin S =1 was seen to show a spontaneous magnetisation.In this case, a first-order phase transition for values of connectivity z = 2 and z = 7 iswell defined. On these same networks the Potts model with q=3 and 8 states is nowstudied through Monte Carlo simulations. We also obtained for q = 3 and 8 states afirst-order phase transition for values of connectivity z = 2 and z = 7 for the directedBarabási-Albert network. Theses results are different from the results obtained for thesame model on two-dimensional lattices, where for q=3 the phase transition is of second order, while for q=8 the phase transition is of first-order.
Keywords: Monte Carlo simulation; Ising; networks; disorder.