title: Many-body theory of synchronization by long-range interactions.
abstract: 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 ψ decays slowly with g0 as |ψ| ∝ g(0)(2).
authors.affiliation: Department of Physics, Tohoku University, Sendai 980-8578, Japan.
authors.forename: Nariya
authors.initials: N
authors.lastname: Uchida
mesh_terms: D008956:Models, Chemical