SELF-CONSISTENT THEORY OF NORMAL-TO-SUPERCONDUCTING TRANSITION

I study the normal-to-superconducting (NS) transition within the Ginzburg-Landau (GL) model, taking into account the fluctuations in the m-component complex order parameter psi(alpha), and the vector potential A in the arbitrary dimension d, for any m. I find that the transition is of second order and that the previous conclusion of the fluctuation-driven first-order transition is a possible artifact of the breakdown of the epsilon-expansion and the inaccuracy of the 1/m-expansion for physical values epsilon = 1, m = 1. I compute the anomalous ri(d, m) exponent at the NS transition, and find eta(3, 1) approximate to - 0.38. In the m--> infinity limit, eta(d, m) becomes exact and agrees with the 1/m-expansion. Near d=4 the theory is also in good agreement with the perturbative E-expansion results for m > 183 and provides a sensible interpolation formula for arbitrary d and m.