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

By considering the large-N Ginzburg-Landau model, compactified in one of the spatial dimensions, we determine the beta-function and find an infrared stable fixed point for a superconducting film for dimensions $4<D<6$. We find that this fixed point is independent of the film thickness ($L$). For the physical dimension D=3 we conclude that if a transition exists it is not a second order one.