Nonequilibrium phase transition due to social group isolation |
Julian M. Sienkiewicz , Janusz A. Hołyst |
Warsaw University of Technology, Faculty of Physics, Koszykowa 75, Warszawa 00-662, Poland |
Abstract |
We introduce a simple model of a growing system with m competing communities [1]. The model corresponds to the phenomenon of defeats suffered by social groups living in isolation. A nonequilibrium phase transition is observed when at critical time t_{c} the first isolated cluster occurs. In the one-dimensional system the volume of the new phase, i.e. the number of the isolated individuals, increases with time as Z~t^{3}. For a large number of possible communities the critical density of filled space equals to ρ_{c} = (m/N)^{1/3} where N is the system size. A similar transition is observed for Erdös-Rényi random graphs and Barabási-Albert scale-free networks. Analytic results are in agreement with numerical simulations.
[1] J. Sienkiewicz, J. A. Hołyst, e-print: arXiv:0807.1984v2 |