Electronic Journal of Probability

Fixation for coarsening dynamics in 2D slabs

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

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Coarsening Glauber Dynamics Ising model

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


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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