Phase transitions in social impact models of opinion formation

We study phase transitions in models of opinion formation which are based on the social impact theory. Two different models are discussed: (i) a cellular–automata based model of a finite group with a strong leader where persons can change their opinions but not their spatial positions, and (ii) a model with persons treated as active Brownian particles interacting via a communication field. In the first model, two stable phases are possible: a cluster around the leader, and a state of social unification. The transition into the second state occurs for a large leader strength and/or for a high level of social noise. In the second model, we find three stable phases, which correspond either to a paramagnetic'' phase (for high noise and strong diffusion), a ferromagnetic’’ phase (for small nose and weak diffusion), or a phase with spatially separated ``domains’’ (for intermediate conditions).