Large-N transition temperature for superconducting films in a magnetic field

Abstract

We consider the N-component Ginzburg-Landau model in large N limit, the system being embedded in an external constant magnetic field and confined between two parallel planes a distance L apart from one another. On physical grounds, this corresponds to a material in the form of a film in the presence of an external magnetic field. Using techniques from dimensional and ζ-function regularization, modified by the external field and the confinement conditions, we investigate the behavior of the system as a function of the film thickness L. This behavior suggests the existence of a minimal critical thickness below which superconductivity is suppressed.