Electronic Journal of Probability

Synchronization for discrete mean-field rotators

Benedikt Jahnel and Christof Külske

Full-text: Open access

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.

Article information

Source
Electron. J. Probab., Volume 19 (2014), paper no. 14, 26 pp.

Dates
Accepted: 20 January 2014
First available in Project Euclid: 4 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465065656

Digital Object Identifier
doi:10.1214/EJP.v19-2948

Mathematical Reviews number (MathSciNet)
MR3164767

Zentralblatt MATH identifier
1288.82042

Subjects
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]

Keywords
Interacting particle systems non-equilibrium synchronization mean-field sytems discretization XY model clock model rotation dynamics attractive limit cycle

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

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


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