title: Thermal fluctuation effects on finite-size scaling of synchronization.
abstract: We consider globally coupled random frequency oscillators under thermal noise, and explore the synchronization transition with its critical behavior near the transition. In particular, we focus on the finite-size scaling behavior of the synchronization, and investigate how the thermal noise affects the correlation size exponent ν of the synchronized oscillators. Extensive numerical simulations as well as mean-field analysis have been performed. We find that the correlation size exponent changes from ν=5/2 without thermal noise to ν=2 with strong thermal noise, where the value ν=2 is the same as that for the usual equilibrium systems described by the Ginzburg-Landau mean-field theory. In order to see the effects of thermal fluctuation further, we remove the frequency-disorder fluctuations originating from the different realizations of natural frequencies of the oscillators, and examine the finite-size scaling behavior for the case only with the thermal fluctuation. It is found that ν becomes 2 at much weak thermal noise strength, which implies that even very weak thermal fluctuations may lead to ν=2 when frequency-disorder fluctuations are absent.
authors.affiliation: Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Korea.
authors.forename: Seung-Woo
authors.initials: SW
authors.lastname: Son
authors.forename: Hyunsuk
authors.initials: H
authors.lastname: Hong