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 ψα 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 ε-expansion and the inaccuracy of the 1/m-expansion for physical values ε = 1, m 1. I compute the anomalous η(d, m) exponent at the NS transition, and find η(3, 1) ∼ -0.38. In the m → ∞ limit, η(d, m) becomes exact and agrees with the 1/m-expansion. Near d = 4 the theory is also in good agreement with the perturbative ε-expansion results for m > 183 and provides a sensible interpolation formula for arbitrary d and m. (orig.)