In the Kuramoto model of infinitely many globally coupled phase oscillators with different frequencies, beyond the synchronization transition the oscillators separate neatly into two groups: an ordered one locked to the mean field, and a disordered one rotating at different frequencies. We show that this picture, valid in the thermodynamic limit of infinite populations, is not exact for finite-sized ensembles, where the mean field fluctuates due to the finite-size effects. We demonstrate that these fluctuations lead to cross-correlations in the disordered group on a microscopic scale. We derive the properties of the cross-correlations analytically under an assumption of white noise fluctuations of the mean field. For finite ensembles where mean field fluctuations are not delta-correlated, cross-correlations are explored numerically in a model that involves active and passive (tracer-type) oscillators.
