  We prove that every non-degenerate minimal submanifold of codimension two can
be obtained as the energy concentration set of a family of critical maps for
the (rescaled) Ginzburg-Landau functional. The proof is purely variational, and
follows the strategy laid out by Jerrard and Sternberg, extending a recent
result for geodesics by Colinet-Jerrard-Sternberg. The same proof applies also
to the $U(1)$-Yang-Mills-Higgs and to the Allen-Cahn-Hilliard energies.
