98-10E

# 98-10E

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 the transition occuring in this model. We use the field-theoretical renormalization group approach and consider the gauge model for a superconductor, generalized to a $n/2$ component complex order parameter. Previuos renormalization group calculations within strict $\varepsilon $-expansion suggested that in such a model a first-order phase transition occurs. We examine expressions for the renormalization group functions in a two-loop approximation in three dimensions. 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 Pad\'e analysis and Pad\'e-Borel resummation technique conclude that in the model under consideration still exists a possibility for the second-order phase transition with critical exponents differing from those of a superfluid liquid. This is in agreement with conclusions made very recently in other nonperturbative treatments.