Critical fluctuations in normal-to-superconducting transition

We study the phase transition to the superconducting state taking into account the fluctuations of the order parameter and of the vector magnetic field and discuss the question of the order of transition occuring in this model. We use the field-theoretical renormalization group approach and consider in two-loop approximation the gauge model for a superconductor, generalized to a n/2 component complex order parameter. Special attention is being payed to the fact, that the corresponding series might be asymptotic ones and therefore have zero radius of convergence. We review different ways of analytical continuation of the series and applying Pade analysis and Pade-Borel resummation technique conclude that in the model under consideration still exists a possibility for the second-order phase transition with the critical exponents differing from those of a superfluid liquid.