## Electronic Journal of Probability

### Fixation for coarsening dynamics in 2D slabs

#### 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

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

Rights

#### 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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