On the dynamics of interfaces in the ferromagnetic XXZ chain under weak   perturbations
  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. 
Bruno Nachtergaele, Wolfgang L Spitzer, Shannon Starr