Lower Critical Dimension for Populations of Oscillators with Randomly Distributed Frequencies: A Renormalization-Group Analysis

Abstract

It is argued by way of a renormalization-group analysis that the lower critical dimension of macroscopic mutual entrainment in a class of populations of oscillators satisfies a certain inequality which is sensitive to the tail of the distribution of native frequencies. This result is supported in part by numerical simulations as well as a proof of the absence of long-range order in one dimension.