Focusing on an order parameter that signals the breakdown of a global symmetry, we employ a dual formulation of the Ginzburg-Landau model to obtain a Landau description of the phase transition of three-dimensional type-II superconductors at zero magnetic field. In the superconducting phase the dual theory is a complex |ψ|4 theory interacting via a shielded Coulomb potential mediated by a massive vector mode which may be pictured as representing the magnetic field. In the normal, high-temperature phase the vector mode decouples and the theory reduces to a pure |ψ|4 theory with a broken global U(1) symmetry. The resulting massless Goldstone mode represents the photon. The phase transition between the two phases is continuous with critical exponents given by those of a superfluid with reversed temperature axis.
Novel results about magnetic fluctuation effects near the normal-to-superconducting phase transition in a zero magnetic field