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  • Open Access

Short-range intervortex forces

Martin Speight*

Thomas Winyard†

  • *Contact author: j.m.speight@leeds.ac.uk
  • †Contact author: twinyard@ed.ac.uk
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Phys. Rev. D 112, 055024 – Published 17 September, 2025

DOI: https://doi.org/10.1103/2m3b-gr79

Abstract

An explicit formula for the interaction energy of n vortices in the Abelian Higgs (or Ginzburg-Landau) model is derived, valid in the regime where all vortices are close to one another. An immediate consequence of this formula is that the interaction energy of a vortex pair with separation d varies as d4, not d2. The formula contains n−1 real coefficients, which are fixed by certain spectral data of the Jacobi operator of the cocentered n-vortex. The coefficients are computed numerically for n=2 and n=3 for couplings 0.1≤λ≤2.5. The resulting short-range interaction potentials are compared with the results of full field theory simulations for λ=0.5 and λ=2, with excellent agreement at small to moderate vortex separation.

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References (16)

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Phys. Rev. D 112, 055024– Published 17 September, 2025
  • Received 24 July 2025
  • Accepted 20 August 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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