Exact Calculation of the Vortex-Antivortex Interaction Energy in the Anisotropic 3D XY-model

摘要

We have developed an exact method to calculate the vortex-antivortexinteraction energy in the anisotropic 3D-XY model. For this calculation, dualtransformation which is already known for the 2D XY-model was extended. Wefound an explicit form of this interaction energy as a function of theanisotropic ratio and the separation $r$ between the vortex and antivortexlocated on the same layer. The form of interaction energy is $\ln r$ at thesmall $r$ limi t but is proportional to $r$ at the opposite limit. This form ofinteraction energ y is consistent with the upper bound calculation using thevariational method by Cataudella and Minnhagen.