Coarsening in 2D slabs

Abstract

We study coarsening; that is, the zero-temperature limit of Glauber dynamics in the standard Ising model on slabs Sk = Z2 × {0,…, k − 1} of all thicknesses k ≥ 2 (with free and periodic boundary conditions in the third coordinate).We show that with free boundary conditions, for k ≥ 3, some sites fixate for large times and some do not, whereas for k = 2, all sites fixate.With periodic boundary conditions, for k ≥ 4, some sites fixate and others do not, while for k = 2 and 3, all sites fixate.