Large-N treatment of the Abrikosov transition at low temperatures
  We investigate the influence of order parameter fluctuations on the transition between normal and mixed superconducting states at low temperatures. We show that in case of clean quasi-two-dimensional superconductors the transition can be described by the functional of the Ginzburg-Landau type. We consider the large-N generalization of this functional and using the lowest Landau level approximation we get the large-N equations which describe the phase transition. In case of physical dimensionality we found that the transition is of the first order. The fluctuations significantly affect the temperature dependence of the upper critical field. 
A.Lopatin, G.Kotliar