On the dynamics of interfaces in the ferromagnetic XXZ chain under weak perturbations

TL;DR

This paper investigates the time evolution of interfaces in the ferromagnetic XXZ chain under weak magnetic perturbations, deriving leading behaviors and corrections in a specific scaling limit.

Contribution

It introduces a scaling limit framework for analyzing interface dynamics in the XXZ chain under weak magnetic fields and computes leading and first correction terms.

Findings

Derived the leading term of interface evolution in the scaling limit

Calculated the first correction to the leading behavior

Analyzed the case of a uniform magnetic field in detail

Abstract

We study the time evolution of interfaces of the ferromagnetic XXZ chain in a magnetic field. A scaling limit is introduced where the strength of the magnetic field tends to zero and the microscopic time to infinity while keeping their product constant. The leading term and its first correction are determined and further analyzed in more detail for the case of a uniform magnetic field.