Synchronization for discrete mean-field rotators
@article{EJP2948,
author = {Benedikt Jahnel and Christof Külske},
title = {Synchronization for discrete mean-field rotators},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {19},
year = {2014},
keywords = {Interacting particle systems; non-equilibrium; synchronization; mean-field sytems; discretization; XY model; clock model; rotation dynamics; attractive limit cycle},
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 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.
},
pages = {no. 14, 1-26},
issn = {1083-6489},
doi = {10.1214/EJP.v19-2948},
url = {http://ejp.ejpecp.org/article/view/2948}}