Spin vortices and vacancies: Interactions and pinning on a square lattice

Abstract

The study gives a decisive answer to the recently risen question about the type and origin of interaction between spin vortices and spin vacancies in 2D spin models. The approach is based on the low-temperature approximation of the 2D XY model known as the Villain model and does not involve any additional approximations, thus preserving the lattice structure. The exact form of the Hamiltonian describing a system of topological charges and a vacant site supports the attractive type of interaction between the vacancy and the charges.The quantitative difference between the characteristics of the vortex behavior in the 2D XY and Villain models due to the different energy of the vortex "cores" in the two models is pointed out. This leads to a conclusion that the interaction between a vortex and a spin vacancy and between a vortex and the antivortex differs quantitatively for small separations in the two mentioned models.