Electronic Journal of Probability
- Electron. J. Probab.
- Volume 19 (2014), paper no. 14, 26 pp.
Synchronization for discrete mean-field rotators
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.
Electron. J. Probab., Volume 19 (2014), paper no. 14, 26 pp.
Accepted: 20 January 2014
First available in Project Euclid: 4 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 82B26: Phase transitions (general) 82C22: Interacting particle systems [See also 60K35]
This work is licensed under a Creative Commons Attribution 3.0 License.
Jahnel, Benedikt; Külske, Christof. Synchronization for discrete mean-field rotators. Electron. J. Probab. 19 (2014), paper no. 14, 26 pp. doi:10.1214/EJP.v19-2948. https://projecteuclid.org/euclid.ejp/1465065656