Anomalous finite-size scaling of synchronization on networks
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)Abstract
We explore the synchronization in networks, with particular attention to the finite-size scaling and configuration-fluctuation effects on it. The scale-free network with degree distribution given by $P(k)k^-\gamma$ is considered, and the collective synchronization is probed for various heterogeneity of the network. Revealed is the configuration-to-configuration fluctuation by quenched disorder plays a crucial role on the finite-size scaling in the synchronization behavior, yielding an unusual correlation exponent $\bar\nu=5/2$ for the mean-field regime with large degree exponent $(\gamma>5)$. Such anomalous exponent is consistent with that for the globally connected networks, which is important for the understanding of synchronization mechanism in complex networks. The criticality for highly heterogeneous regime $(\gamma<5)$ is also investigated, where the scaling exponent is found to be $\gamma$ dependent. We perform the extensive numerical simulations, and show a good consistency with the theoretical prediction by configuration-fluctuation effects.