The inverted XY universality of the superconductivity phase transition
  It has been conjectured that the phase transition in the Ginzburg-Landau theory is dual to the XY model transition. We study numerically a particular limit of the GL theory where this duality becomes exact, clarifying some of the problems encountered in standard GL theory simulations. This may also explain the failure of the superconductor experiments to observe the XY model scaling. 
Thomas Neuhaus, Arttu Rajantie and Kari Rummukainen