  Irreversible opinion spreading phenomena are studied on small-world and
scale-free networks by means of the magnetic Eden model, a nonequilibrium
kinetic model for the growth of binary mixtures in contact with a thermal bath.
In this model, the opinion of an individual is affected by those of their
acquaintances, but opinion changes (analogous to spin flips in an Ising-like
model) are not allowed. We focus on the influence of advertising, which is
represented by external magnetic fields. The interplay and competition between
temperature and fields lead to order-disorder transitions, which are found to
also depend on the link density and the topology of the complex network
substrate. The effects of advertising campaigns with variable duration, as well
as the best cost-effective strategies to achieve consensus within different
scenarios, are also discussed.
