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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.

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
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