Groupe de Physique Statistique/ Arbeitsgruppe Statistische Physik

The synchronization transition of coupled random frequency oscillators is revisited. The Kuramoto model (global coupling) is shown to exhibit unusual sample-dependent finite size effects leading to a correlation size exponent \bar\nu=5/2. This is generalized to scale-free networks where more interesting finite-size scaling is observed. Simulations of locally coupled oscillators in d-dimensions reveal two types of frequency entrainment: mean-field behavior at d>4, and aggregation of compact synchronized domains in three and four dimensions. In the latter case, scaling arguments yield a correlation length exponent \nu=2/(d-2), in good agreement with numerical results.