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Fixation for coarsening dynamics in 2D slabs. (English) Zbl 1284.82038
Summary: 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 reach 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.

##### MSC:
 82C20 Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics 60K35 Interacting random processes; statistical mechanics type models; percolation theory 82B43 Percolation
##### Keywords:
coarsening; Glauber dynamics; Ising model
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