Open Access
2013 Fixation for coarsening dynamics in 2D slabs
Michael Damron, Hana Kogan, Charles Newman, Vladas Sidoravicius
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Electron. J. Probab. 18: 1-20 (2013). DOI: 10.1214/EJP.v18-3059


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.


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Michael Damron. Hana Kogan. Charles Newman. Vladas Sidoravicius. "Fixation for coarsening dynamics in 2D slabs." Electron. J. Probab. 18 1 - 20, 2013.


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

zbMATH: 1284.82038
MathSciNet: MR3145052
Digital Object Identifier: 10.1214/EJP.v18-3059

Primary: 60K35
Secondary: 82B43

Keywords: coarsening , Glauber dynamics , Ising model

Vol.18 • 2013
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