Short-range intervortex forces

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.