Synchronization of coupled oscillators on a d-dimensional lattice with the power-law coupling G(r)=g0/rα and randomly distributed intrinsic frequency is analyzed. A systematic perturbation theory is developed to calculate the order parameter profile and correlation functions in powers of ε=α/d-1. For α≤d, the system exhibits a sharp synchronization transition as described by the conventional mean-field theory. For α>d, the transition is smeared by the quenched disorder, and the macroscopic order parameter ψ̄ decays slowly with g0 as |ψ̄| g02.
ASJC Scopus subject areas
- Physics and Astronomy(all)