Localization of spin excitations in a uniaxial ferromagnet with rapidly decreasing exchange potential

The concept of self-localization is applied to a uniaxial ferromagnet. Conditions and criteria of localization for four crystal lattices are obtained by perturbation theory. The part played by regularity of the system is established. The authors consider the case of a high particle concentration. The interaction is assumed to decrease rapidly, i.e., is effective at a few interatomic distances. In parallel they also analyze irregular systems in which disorder in the interaction is due not only to thermal spread of the particle positions but also fluctuations of the exchange interaction. It is convenient to choose the anisotropic Heisenberg model as a model problem for investigating localization