Nonequilibrium phase transition due to isolation of communities

Julian Sienkiewicz and Janusz A. Hołyst
Phys. Rev. E 80, 036103 – Published 2 September 2009

Abstract

We introduce a simple model of a growing system with m competing communities. 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 Zt3. For a large number of possible communities, the critical density of filled space is equal to ρc=(m/N)1/3, where N is the system size. A similar transition is observed for Erdős-Rényi random graphs and Barabási-Albert scale-free networks. Analytical results are in agreement with numerical simulations.

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  • Received 16 September 2008

DOI:https://doi.org/10.1103/PhysRevE.80.036103

©2009 American Physical Society

Authors & Affiliations

Julian Sienkiewicz and Janusz A. Hołyst

  • Faculty of Physics, Center of Excellence for Complex Systems Research, Warsaw University of Technology, Koszykowa 75, PL-00-662 Warsaw, Poland

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Issue

Vol. 80, Iss. 3 — September 2009

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