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
Warsaw University of Technology, Centre of Excellence for Complex Systems Research, 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 tc 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~t3. For a large number of possible communities the critical density of filled space equals to ρc = (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

 

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Presentation: Oral at 4 Ogólnopolskie Sympozjum "Fizyka w Ekonomii i Naukach Społecznych", by Julian M. Sienkiewicz
See On-line Journal of 4 Ogólnopolskie Sympozjum "Fizyka w Ekonomii i Naukach Społecznych"

Submitted: 2009-03-10 11:23
Revised:   2009-06-07 00:48