Dresden 2009 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 12: Poster I
DY 12.24: Poster
Tuesday, March 24, 2009, 14:30–16:30, P1A
Nonequilibrium phase transitions in finite arrays of globally coupled Stratonovich models: Strong coupling limit — Fabian Senf, •Philipp M. Altrock, and Ulrich Behn — Institut für Theoretische Physik, Universität Leipzig, Deutschland
A finite array of N globally coupled Stratonovich models exhibits a continuous nonequilibrium phase transition. In the limit of strong coupling there is a clear separation of time scales of center of mass and relative coordinates. The latter relax very fast to zero and the array behaves as a single entity described by the center of mass coordinate. We compute analytically the stationary probability and the moments of the center of mass coordinate. The scaling behavior of the moments near the critical value of the control parameter ac(N) is determined. We identify a crossover from linear to square root scaling with increasing distance from ac. The crossover point approaches ac in the limit N → ∞ which reproduces previous results for infinite arrays. The results are obtained in both the Fokker-Planck and the Langevin approach and are corroborated by numerical simulations. For a general class of models we show that the transition manifold in the parameter space depends on N and is determined by the scaling behavior near a fixed point of the stochastic flow.