Non-nequilibrium model on Apollonian networks
  We investigate the Majority-Vote Model with two states ($-1,+1$) and a noise $q$ on Apollonian networks. The main result found here is the presence of the phase transition as a function of the noise parameter $q$. We also studies de effect of redirecting a fraction $p$ of the links of the network. By means of Monte Carlo simulations, we obtained the exponent ratio $\gamma/\nu$, $\beta/\nu$, and $1/\nu$ for several values of rewiring probability $p$. The critical noise was determined $q_{c}$ and $U^{*}$ also was calculated. The effective dimensionality of the system was observed to be independent on $p$, and the value $D_{eff} \approx1.0$ is observed for these networks. Previous results on the Ising model in Apollonian Networks have reported no presence of a phase transition. Therefore, the results present here demonstrate that the Majority-Vote Model belongs to a different universality class as the equilibrium Ising Model on Apollonian Network. 
F. W. S. Lima, Andr\'e A. Moreira, Asc\^anio D. Ara\'ujo
physics.soc-ph cs.SI