Co-evolution of the Potts model and topology of interactions

Joanna Toruniewska ,  Krzysztof Suchecki ,  Janusz A. Hołyst 

Warsaw University of Technology, Faculty of Physics and Cent.of Exc.for Complex Systems Research, Koszykowa 75, Warszawa 00-662, Poland

Abstract

Discrete q-state Potts model with network dynamics, described by the canonical ensemble has been considered. Three states have been found in the system. Fragmented network (ordered clusters state) is one of them and it has been found unstable - after a sufficiently long time the system arrives at a stable globally ordered state. It has been found that the system orders through the near-linear growth of the largest clusters. Based on the observation of the results it has been found that growth of the largest cluster is caused by state dynamics. The analytical prediction of growth of that cluster has been proposed. The prediction is based on transfer of surface nodes from smaller to larger clusters. Only surface nodes (nodes with only one connection in their cluster) participate in this process. The surface size is not predicted analytically, but is a required input from numerical simulation to correctly reproduce observed behavior. Analytical description correctly describes the transition from the local to the global ordered state.

 

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Presentation: Poster at 8 Ogólnopolskie Sympozjum "Fizyka w Ekonomii i Naukach Społecznych", by Joanna Toruniewska
See On-line Journal of 8 Ogólnopolskie Sympozjum "Fizyka w Ekonomii i Naukach Społecznych"

Submitted: 2015-09-03 19:25
Revised:   2015-09-03 20:43