Fixation for coarsening dynamics in 2D slabs

Michael Damron (Indiana University)
Hana Kogan (New York University)
Charles M. Newman (New York University)
Vladas Sidoravicius (IMPA)


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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Pages: 1-20

Publication Date: December 17, 2013

DOI: 10.1214/EJP.v18-3059


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