Simulations of the 3d Ginzburg-Landau Model with Soft Amplitudes
  Using cluster Monte Carlo simulations, the 3d complex Ginzburg-Landau model reveals a first order transition when the amplitude of the complex field is sufficiently soft, i.e. adapts itself to the phase configurations of the field. This transition is driven by phase fluctuations in agreement with a previous analytical approach. 
Philippe Curty, Hans Beck