Dynamics of an Unbounded Interface Between Ordered Phases

TL;DR

This paper studies the evolution of unbounded interfaces in 2D Ising ferromagnets with zero-temperature Glauber dynamics, revealing self-similar limiting shapes and connecting microscopic and continuum models.

Contribution

It introduces a combined microscopic and continuum approach to analyze interface evolution, including a novel link to Young tableaux for single-corner cases.

Findings

Interfaces evolve to self-similar shapes

Continuum and microscopic models agree on interface shape

Connection established between interface dynamics and Young tableaux

Abstract

We investigate the evolution of a single unbounded interface between ordered phases in two-dimensional Ising ferromagnets that are endowed with single-spin-flip zero-temperature Glauber dynamics. We examine specifically the cases where the interface initially has either one or two corners. In both examples, the interface evolves to a limiting self-similar form. We apply the continuum time-dependent Ginzburg-Landau equation and a microscopic approach to calculate the interface shape. For the single corner system, we also discuss a correspondence between the interface and the Young tableau that represents the partition of the integers.