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It is well-known that under suitable hypotheses, for a sequence of solutions of the (simplified) Ginzburg–Landau equations-\Delta u_{\varepsilon} +\varepsilon^{-2}(|u_{\varepsilon}|^{2}-1)u_{\varepsilon} = 0, the energy and vorticity concentrate as\varepsilon\to 0around a codimension2stationary varifold – a (measure-theoretic) minimal surface. Much less is known about the question of whether, given a codimension2minimal surface, there exists a sequence of solutions for which the given minimal surface is the limiting concentration set. The corresponding question is very well-understood for minimal hypersurfaces and the scalar Allen–Cahn equation, and for the Ginzburg–Landau equations when the minimal surface is locally area-minimizing, but otherwise quite open. We consider this question on a3-dimensional closed Riemannian manifold(M,g), and we prove that any embedded nondegenerate closed geodesic can be realized as the asymptotic energy/ vorticity concentration set of a sequence of solutions of the Ginzburg–Landau equations.