Coarsening in 2D slabs

TL;DR

This paper investigates the coarsening dynamics of the zero-temperature Glauber process in 2D Ising slabs, revealing how boundary conditions and slab thickness influence site fixation over time.

Contribution

It provides a detailed analysis of fixation phenomena in 2D Ising slabs under different boundary conditions and thicknesses, highlighting new behaviors in coarsening dynamics.

Findings

For free boundary conditions, some sites fixate for k ≥ 3, others do not.

For free boundary conditions with k=2, all sites fixate.

With periodic boundary conditions, fixation depends on slab thickness, with some sites fixating for k ≥ 4 and all sites fixating for k=2 and 3.

Abstract

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