Regensburg 2007 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 6: Statistical physics of complex networks II

DY 6.2: Talk

Monday, March 26, 2007, 14:45–15:00, H3

Ising model on two connected Barabasi-Albert networks — •Krzysztof Suchecki and Janusz Hołyst — Faculty of Physics and Center of Excellence for Complex Systems Research, Warsaw University of Technology, Koszykowa 75, PL-00-662 Warsaw, Poland

We have investigated analytically the behavior of Ising model on two connected Barabasi-Albert networks. Depending on the temperature and the number of inter-network connections, the system can order in one or two possible phases. In the first phase both networks are ordered paralelly. In the second phase there is a ferromagnetic order inside each networks and antiparallel order between them.

At low temperatures both phases can exist depending on initial conditions. At a certain critical temperature Tc-, the antiparallel state becomes unstable and one of the networks reverses its magnetization. This is a first order phase transition. At a higher temperature Tc+ the networks do not maintain common ordering, and the system becomes paramagnetic. This is a standard second order phase transition.

Both critical temperatures Tc- and Tc+ depend on network size and internetwork connections ratio p, defined as amount of internetwork links to intranetwork links. While Tc+ increases with p in linear fashion, the dependence Tc- on p is much more complex, but strictly decreasing. At p=1 the temperature Tc-=0.

Analytic calculations of critical temperatures, based on a mean field approach, are in qualitative agreement with Monte Carlo simulations of above systems.