Electronic Journal of Probability

Fixation for coarsening dynamics in 2D slabs

Michael Damron, Hana Kogan, Charles Newman, and Vladas Sidoravicius

Full-text: Open access

Abstract

We study zero-temperature Ising Glauber Dynamics, on $2D$ slabs of thickness $k \geq 2$. In this model, $\pm 1$-valued spins at integer sites update according to majority vote dynamics with two opinions. We show that all spins reaches a final state (that is, the system fixates) for $k=2$ under free boundary conditions and for $k=2$ or $3$ under periodic boundary conditions. For thicker slabs there are sites that fixate and sites that do not.

Article information

Source
Electron. J. Probab., Volume 18 (2013), paper no. 105, 20 pp.

Dates
Accepted: 17 December 2013
First available in Project Euclid: 4 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465064330

Digital Object Identifier
doi:10.1214/EJP.v18-3059

Mathematical Reviews number (MathSciNet)
MR3145052

Zentralblatt MATH identifier
1284.82038

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 82B43: Percolation [See also 60K35]

Keywords
Coarsening Glauber Dynamics Ising model

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

Citation

Damron, Michael; Kogan, Hana; Newman, Charles; Sidoravicius, Vladas. Fixation for coarsening dynamics in 2D slabs. Electron. J. Probab. 18 (2013), paper no. 105, 20 pp. doi:10.1214/EJP.v18-3059. https://projecteuclid.org/euclid.ejp/1465064330


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