Physica A 285 (2000) 199-210
Abstract of the article

Phase transitions in social impact models of opinion formation


Janusz A. Hołyst 1,2,3 Krzysztof Kacperski 1,3 Frank Schweitzer 2,4
1 Faculty of Physics, Warsaw University of Technology, Koszykowa 75, PL-00-662 Warsaw, Poland
2 Institute of Physics, Humboldt University, Unter den Linden 6, D-10099 Berlin, Germany
3 Max Planck Institute for Physics of Complex Systems, Nöthnitzer Str. 38, D-01187 Dresden, Germany
4 Real World Computing Partnership, Theoretical Foundation GMD Laboratory, Schloss Birlinghoven, D-53754 Sankt Augustin, Germany

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).