Finite-size scaling of the Kuramoto model at criticality

The asymptotic scaling behavior of the Kuramoto model with finite populations has been notably elusive, despite comprehensive investigations employing both analytical and numerical methods. In this paper, we explore the Kuramoto model with "deterministic" sampling of natural frequencies, employing extensive numerical simulations and reporting the asymptotic values of the finite-size scaling exponents, which deviate significantly from the previously reported values in the literature. Additionally, we observe that these exponents are sensitive to the specifics of the sampling method. We discuss the origins of this variability through the self-consistent theory of entrained oscillators.