Non-equilibrium BCS model on Apollonian networks

Abstract

We study the phase transition in a discrete opinion dynamics model on an Apollonian network, where mutual interactions can be both positive and negative depending on the noise parameter q. We have characterized the critical exponents of the phase transitions through the Monte Carlo simulations and finite-size scaling analysis. Our finds attest that different from the equilibrium models, such as Ising and Potts on Apollonian network that do not present phase transition, the kinetic model report does. Moreover, we have included one additional aspect on the Apollonian network, the effect of redirecting a fraction of p of the network’s links. On this redirected network, we obtained the exponents ratio β∕ν, γ∕ν, and 1∕ν for several values of rewiring probability p. Similar to this model’s results on free-scale networks, the effective dimensionality of the system found was Deff≈1.0 for all values of p. The results presented here demonstrate that kinetic models of discrete opinion dynamics belong to a different universality class as the equilibrium Ising Model on Apollonian networks. It is noticed that the kinetic model study here and the majority-vote model on Apollonian networks are in the same universality class, for a rewiring probability lower than 0.5. Above p=0.5, the critical exponents are different from those found in the majority-vote model on Apollonian networks.