Exact calculation of the vortex-antivortex interaction energy in the anisotropic three-dimensional XY model

We have developed an exact method to calculate the vortex-antivortex interaction energy in the anisotropic three-dimensional (3D) XY model. For this calculation, dual transformation, which is already known for the 2D XY model, was extended. We found an explicit form of this interaction energy as a function of the anisotropic ratio and the separation r between the vortex and antivortex located on the same layer. The form of the interaction energy is ln r at the small r limit but is proportional to r at the opposite limit. This form of interaction energy is consistent with the upper-bound calculation using the variational method by Cataudella and Minnhagen.