Slow Coarsening in an Ising Chain with Competing Interactions

TL;DR

This paper studies the slow zero-temperature coarsening process in an Ising chain with competing ferromagnetic and antiferromagnetic interactions, revealing a decay rate of t^{-1/n} driven by multispecies excitations.

Contribution

It introduces a detailed analysis of the coarsening dynamics in an Ising chain with competing interactions, identifying elementary excitations and their decay rates, and establishing the slow approach to the ground state.

Findings

Coarsening follows a t^{-1/n} decay law.

Elementary excitations are identified as domains of n+1 spins.

The dominant process involves (n+1)-particle annihilation.

Abstract

We investigate the zero-temperature coarsening dynamics of a chain of Ising spins with a nearest-neighbor ferromagnetic and an nth-neighbor antiferromagnetic interactions. For sufficiently large antiferromagnetic interaction, the ground state consists of $n$ consecutive up spins followed by n down spins, etc. We show that the asymptotic coarsening into this ground state is governed by a multispecies reactive gas of elementary excitations. The basic elementary excitations are identified and each decays at a different power-law rate in time. The dominant excitations are domains of n+1 spins which diffuse freely and disappear through processes which are effectively governed by (n+1)-particle annihilation. This implies that the ground state is approached slowly with time, as t^{-1/n}.