Large-N $\beta$-function for superconducting films in a magnetic field

TL;DR

This paper analyzes the large-N Ginzburg-Landau model for superconducting films, deriving a beta-function and identifying a stable fixed point in certain dimensions, with implications for phase transition nature.

Contribution

It introduces a large-N approach to the Ginzburg-Landau model for superconducting films, revealing a fixed point independent of film thickness.

Findings

Identifies an infrared stable fixed point for 4<D<6

Fixed point is independent of film thickness L

Suggests no second-order transition for D=3

Abstract

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.