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

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

1995-03-13

arxiv.org/abs/cond-mat/9503066v1

Physics

Condensed Matter

REVTeX 12 pages, In print for publication in Phys. Rev. B

Scientific paper

10.1103/PhysRevB.51.6680

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 $\ln r$ 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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