Nonequilibrium model on Apollonian networks.

We investigate the majority-vote model with two states (-1,+1) and a noise parameter q on Apollonian networks. The main result found here is the presence of the phase transition as a function of the noise parameter q. Previous results on the Ising model in Apollonian networks have reported no presence of a phase transition. We also studied the effect of redirecting a fraction p of the links of the network. By means of Monte Carlo simulations, we obtained the exponent ratio γ/ν, β/ν, and 1/ν for several values of rewiring probability p. The critical noise q{c} and U were also calculated. Therefore, the results presented here demonstrate that the majority-vote model belongs to a different universality class than equilibrium Ising model on Apollonian network.