Exact Calculation of the Vortex-Antivortex Interaction Energy in the Anisotropic 3D XY-model
Mahn-Soo Choi, Sung-Ik Lee
Abstract
We have developed an exact method to calculate the vortex-antivortex interaction energy in the anisotropic 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 interaction energy is r at the small r limi t but is proportional to r at the opposite limit. This form of interaction energ y is consistent with the upper bound calculation using the variational method by Cataudella and Minnhagen.
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