Lower Critical Dimension for Populations of Oscillators with Randomly Distributed Frequencies: A Renormalization-Group Analysis
- 11 July 1988
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 61 (2), 231-234
- https://doi.org/10.1103/physrevlett.61.231
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.Keywords
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