Zusammenfassung
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 beta/nu, gamma/nu, and 1/nu 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 D-eff approximate
to 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. Published by Elsevier B.V.
Nutzer