Finite-size effects in a population of interacting oscillators

We consider a large population of globally coupled noisy phase oscillators. In the thermodynamic limit →N∞ this system exhibits a nonequilibrium phase transition, at which a macroscopic mean field appears. It is shown that for large but finite system size N the system can be described by the noisy Stuart-Landau equation, yielding scaling behavior of statistical characteristics of the macroscopic mean field with N. The predictions of the theory are checked numerically.