Electronic Journal of Probability
- Electron. J. Probab.
- Volume 17 (2012), paper no. 26, 40 pp.
The role of disorder in the dynamics of critical fluctuations of mean field models
The purpose of this paper is to analyze how disorder affects the dynamics of critical fluctuations for two different types of interacting particle system: the Curie-Weiss and Kuramoto model. The models under consideration are a collection of spins and rotators respectively. They both are subject to a mean field interaction and embedded in a site-dependent, i.i.d. random environ- ment. As the number of particles goes to infinity their limiting dynamics become deterministic and exhibit phase transition. The main result con- cerns the fluctuations around this deterministic limit at the critical point in the thermodynamic limit. From a qualitative point of view, it indicates that when disorder is added spin and rotator systems belong to two different classes of universality, which is not the case for the homogeneous models (i.e., without disorder).
Electron. J. Probab., Volume 17 (2012), paper no. 26, 40 pp.
Accepted: 23 March 2012
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: 82C44: Dynamics of disordered systems (random Ising systems, etc.)
This work is licensed under aCreative Commons Attribution 3.0 License.
Collet, Francesca; Dai Pra, Paolo. The role of disorder in the dynamics of critical fluctuations of mean field models. Electron. J. Probab. 17 (2012), paper no. 26, 40 pp. doi:10.1214/EJP.v17-1896. https://projecteuclid.org/euclid.ejp/1465062348