Frustrated Synchronization of the Kuramoto Model on Complex Networks.

We present a synchronization transition study of the locally coupled Kuramoto model on extremely large graphs. We compare regular 405 and 1004 lattice results with those of 12,0002 lattice substrates with power-law decaying long links (ll). The latter heterogeneous network exhibits ds>4 spectral dimensions. We show strong corrections to scaling and mean-field type of criticality at d=5, with logarithmic corrections at d=4 Euclidean dimensions. Contrarily, the ll model exhibits a non-mean-field smeared transition, with oscillating corrections at similarly high spectral dimensions. This suggests that the network heterogeneity is relevant, causing frustrated synchronization akin to Griffiths effects.