Nonequilibrium phase transition due to isolation of communities.
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.
Sienkiewicz
Julian
J
Faculty of Physics, Center of Excellence for Complex Systems Research, Warsaw University of Technology, Koszykowa 75, PL-00-662 Warsaw, Poland.
Hołyst
Janusz A
JA
D003163:Competitive Behavior / Q000502:physiology*; D003198:Computer Simulation; D008954:Models, Biological; D044367:Phase Transition; D011157:Population Dynamics; D012919:Social Behavior