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.