On the critical fluctuations in superconductors

The field-theoretical gauge model for a superconductor, generalized to an n/2-component complex order parameter is considered. The question of the order of the phase transition occurring in this model is discussed. Previous renormalization-group calculations suggest that in such a model a fluctuation-induced first-order phase transition occurs. We reexamine previously obtained expressions for the renormalization-group functions in the two-loop approximation in three dimensions. Special attention is being paid to the fact that the corresponding series might be the asymptotic ones and therefore have zero radius of convergence. We discuss the possible ways of analytical continuation of the series obtained. Comparing results obtained by 'direct' calculations with those obtained by Pade analysis and the Pade-Borel resummation technique, the conjecture is made that in the model under consideration there still exists a possibility for a second-order phase transition.