Irreversible Opinion Spreading on Scale-Free Networks

We study the dynamical and critical behavior of a model for irreversible opinion spreading on Barab\'asi-Albert (BA) scale-free networks by performing extensive Monte Carlo simulations. The opinion spreading within an inhomogeneous society is investigated by means of the magnetic Eden model, a nonequilibrium kinetic model for the growth of binary mixtures in contact with a thermal bath. The deposition dynamics, which is studied as a function of the degree of the occupied sites, shows evidence for the leading role played by hubs in the growth process. Systems of finite size grow either ordered or disordered, depending on the temperature. By means of standard finite-size scaling procedures, the effective order-disorder phase transitions are found to persist in the thermodynamic limit. This critical behavior, however, is absent in related equilibrium spin systems such as the Ising model on BA scale-free networks, which in the thermodynamic limit only displays a ferromagnetic phase. The dependence of these results on the degree exponent is also discussed for the case of uncorrelated scale-free networks.