First Order Transition in the Ginzburg-Landau Model
  The d-dimensional complex Ginzburg-Landau (GL) model is solved according to a variational method by separating phase and amplitude. The GL transition becomes first order for high superfluid density because of effects of phase fluctuations. We discuss its origin with various arguments showing that, in particular for d = 3, the validity of our approach lies precisely in the first order domain. 
Philippe Curty, Hans Beck