Synchronization for discrete mean-field rotators

Benedikt Jahnel (Ruhr-Universität Bochum)
Christof Külske (Ruhr-Universität Bochum)


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 which provides an example of a non-ergodic interacting particle system on the basis of a mechanism suggested by Maes and Shlosman.

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.

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Pages: 1-26

Publication Date: January 20, 2014

DOI: 10.1214/EJP.v19-2948


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