  We investigate the role of opinion leaders or influentials in the collective
behavior of a social system. Opinion leaders are characterized by their
unidirectional influence on other agents. We employ a model based on Axelrod's
dynamics for cultural interaction among social agents that allows for
non-interacting states. We find three collective phases in the space of
parameters of the system, given by the fraction of opinion leaders and a
quantity representing the number of available states: one ordered phase having
the state imposed by the leaders; another nontrivial ordered phase consisting
of a majority group in a state orthogonal or alternative to that of the opinion
leaders, and a disordered phase, where many small groups coexist. We show that
the spontaneous rise of an alternative group in the presence of opinion leaders
depends on the existence of a minimum number of long-range connections in the
underlying network. This phenomenon challenges the common idea that
influentials are fundamental to propagation processes in society, such as the
formation of public opinion.
