2008/07/31 by Julian Sienkiewicz, Janusz A. Hołyst, Janusz A. Holyst
Chemistry · Physics and Astronomy · Social Sciences · #Biology #Business #Chemistry #Complex Network Analysis Techniques #Condensed matter physics #Evolutionary Game Theory and Cooperation #Isolation (microbiology) #Non-equilibrium thermodynamics #Opinion Dynamics and Social Influence #Phase (matter) #Phase transition #Physics #Quantum mechanics #Statistical physics #Thermodynamics #Transition (genetics) #physics.comp-ph #physics.soc-ph
paper · pdf · doi:10.1103/physreve.80.036103
published as Phys. Rev. E 80, 036103 (2009) · 5 pages, 4 figures
arxiv created 2009/02/25 · openalex publication_date 2009/09/02 · arxiv updated 2011/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 Z approximately t3. For a large number of possible communities, the critical density of filled space is equal to rho(c)=(m/N)1/3, where N is the system size. A similar transition is observed for Erdos-Rényi random graphs and Barabási-Albert scale-free networks. Analytical results are in agreement with numerical simulations.