Thermodynamic limit of the first-order phase transition in the Kuramoto model
Thermodynamic limit of the first-order phase transition in the Kuramoto model
In the Kuramoto model, a uniform distribution of the natural frequencies leads to a first-order (i.e., discontinuous) phase transition from incoherence to synchronization, at the critical coupling parameter K(c). We obtain the asymptotic dependence of the order parameter above criticality: r-r(c)alpha(K - K(c))(2/3). For a finite population, we demonstrate that …