Prog. Theor. Phys. Vol. 75 No. 6 (1986) pp. 1319-1327
Cooperative Phenomena in Two-Dimensional Active Rotator Systems
Research Institute for Fundamental Physics, Kyoto University, Kyoto 606
*Department of Physics, Kyoto University, Kyoto 606
(Received February 20, 1986)
Phase transitions of active rotator systems with short-range coupling are discussed. The constituents of the system which we call active rotators are represented by a phase model of a limit-cycle oscillator or an excitable element, i.e., dφ/dt=ω-bsin
φ, (|ω/b|>1 or <1). The rotators are subject to noises, and ferromagnetic type coupling is assumed between them. The effect of infinitesimal noises on a perfectly ordered motion is examined for various spatial dimensions by using a linear approximation. As a result, a macroscopic in-phase oscillation throughout the system turned out impossible for 1 and 2 dimensions, but possible for 3 dimensions. An interesting feature expected for a two-dimensional system is that there is a finite parameter region where characteristic length scale is absent. In order to see the latter feature in more detail, we performed a Langevin simulation for a two-dimensional system, and confirmed the existence of a Kosterlitz-Thouless type parameter region.
DOI : 10.1143/PTP.75.1319
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Citing Article(s) :
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