Theory of defect states in the two-dimensional planar rotator model with long-range interaction

The interaction law for defect states of the vortex-pair type in the planar rotator model with long-range interaction 1rα and 2⩽α⩽4, is derived. It is shown that the constituents of a vortex-pair do not interact via a log r law as it is the case for the short-range interaction but are more tightly bound. Furthermore the concept of the state of excitation of a vortex-pair is developed. The consequences of this theory for the character of the phase transition in these models is discussed.