The aim of this paper is twofold. On the one hand we present a brief overview on the application of statistical physics methods to the modelling of social phenomena focusing our attention on models for opinion formation. On the other hand, we discuss and present original results of a model for opinion formation based on the social impact theory developed by Latané. The presented model accounts for the interaction among the members of a social group under the competitive influence of a strong leader and the mass media, both supporting two different states of opinion. Extensive simulations of the model are presented, showing that they led to the observation of a rich scenery of complex behaviour including, among others, critical behaviour and phase transitions between a state of opinion dominated by the leader and another dominated by the mass media. The occurrence of interesting finite-size effects reveals that, in small communities, the opinion of the leader may prevail over that of the mass media. This observation is relevant for the understanding of social phenomena involving a finite number of individuals, in contrast to actual physical phase transitions that take place in the thermodynamic limit. Finally, we give a brief outlook of open questions and lines for future work.

The dynamic behavior of a social group influenced by both a strong leader and the mass media, which is modeled according to the social impact theory, is studied under two situations: (i) The strong leader changes his/her state of opinion periodically while the mass media are not considered. In this case, the leader is capable of driving the group between a dynamically ordered state with a weak leader-group coupling (high-frequency regime) and a dynamically disordered state where the group follows the opinion of the leader (low-frequency regime). (ii) The mass-media change periodically their message and have to compete with a strong leader that keeps his/her state of opinion unchanged. In this case, the mass media require an amplitude threshold in order to overcome the influence of the leader and drive the system into a dynamically disordered state. The dynamic behavior characteristic of the studied social opinion model shares many features of physical systems that are relevant in the fields of statistical mechanics and condensed matter.