Large-N β function for superconducting films in a magnetic field

By considering the large-N Ginzburg-Landau model, compacted in one of the spatial dimensions, we determine the beta function and find an infrared stable fixed point for a superconducting film in presence of an external magnetic field, for dimensions 4<D<6. We find that this fixed point is independent of the film thickness (L). For D≤4, severe infrared divergences appearing under the form of divergence of the integral in the quantity a(D), defined after Eq. (14), forbid an analogous analysis. For the physical dimension D=3 we conclude that if a transition exists, it should not be a second-order one