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

TL;DR

This paper investigates the interaction between spin vortices and vacancies in 2D spin models, revealing an attractive interaction and differences in vortex behavior between the XY and Villain models due to core energy variations.

Contribution

It provides an exact Hamiltonian description of vortex-vacancy interactions in the Villain model without additional approximations, clarifying the nature of these interactions.

Findings

Vortex-vacancy interaction is attractive.

Differences in vortex behavior are due to core energy variations.

Quantitative differences exist between XY and Villain models at small separations.

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.