Synchronization for discrete mean-field rotators

Abstract

We analyze a non-reversible mean-field jump dynamics for discrete q-valued rotators and show in particular that it exhibits synchronization. The dynamics is the mean-field analogue of the lattice dynamics investigated by the same authors in [26] which provides an example of a non-ergodic interacting particle system on the basis of a mechanism suggested by Maes and Shlosman [32]. Based on the correspondence to an underlying model of continuous rotators via a discretization transformation we show the existence of a locally attractive periodic orbit of rotating measures. We also discuss global attractivity, using a free energy as a Lyapunov function and the linearization of the ODE which describes typical behavior of the empirical distribution vector.

29 pages, 3 figures

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Cited by in corpus (2)

• Gibbsian and non-Gibbsian properties of the generalized mean-field fuzzy Potts-model
• A class of nonergodic interacting particle systems with unique invariant measure