Phase Transitions of the Majority-Vote Model with Inertia on Directed Erdös-Rényi Networks.

The phase transition of the majority vote model with inertia has been investigated by means of extensive Monte Carlo simulations on directed Erdös-Rényi networks. Besides the usual average connectivity and local field that adds the opinion of the site itself, an additional term of inertia is considered. The relaxation time of the average opinion state of the network, together with the average opinion state fourth-order Binder cumulant and the corresponding opinion state susceptibility, have been analyzed for several different network sizes and local field and inertia parameter values, for average connectivity of 20 connections. The present results show that the phase transition of this model strongly depends on the inertia parameter, being quite different and richer than previous results of the same model on other regular networks. For inertia parameters between zero and 0.1 the system undergoes a continuous phase transition; for values in the range 0.1 and 0.2 no transition can be seen; for still larger values of inertia up to 0.5 a first-order phase transition takes place; finally, for values larger than 0.5 the dynamics is fully dominated by the inertia, and again no phase transition is observed.