Regensburg 2010 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 23: Networks: From Topology to Dynamics III (joint session of BP, DY, SOE)
DY 23.4: Talk
Thursday, March 25, 2010, 11:00–11:15, H44
Coupled Order Parameter Systems on Scale-free Networks — •Christian von Ferber1,2, Reinhard Folk3, Vasyl Palchykov4, and Yurij Holovatch3,4 — 1Applied Mathematics Research Centre, Coventry University, UK — 2Physikalisches Institut, Universität Freiburg — 3Institut für Theoretische Physik, Universität Linz, AT — 4Institute for Condensed Matter Physics, Lviv, UA
We analyse a system of two scalar order parameters on a complex scale-free network in the spirit of Landau theory. To add a microscopic background to the phenomenological approach we also study a particular spin Hamiltonian that leads to coupled scalar order behavior using the mean field approximation. This set up may describe a model of opinion formation where e.g. opinions on a party a candidate are coupled. Our results show that the system is characterised by either of two types of ordering: either one of the two order parameters is zero or both are non-zero but have the same value. While the critical exponents do not differ from those of a model with a single order parameter on a scale free network there are notable differences for the amplitude ratios and susceptibilities. Another peculiarity of the model is that the transverse susceptibility is divergent at all T < Tc when O(n) symmetry is present. This behavior is related to the appearance of Goldstone modes.