A note on the infrared behavior of the compactified Ginzburg--Landau model in a magnetic field

TL;DR

This paper analyzes the infrared behavior of the large-N Ginzburg--Landau model with compactified dimensions under a magnetic field, revealing an infrared-stable fixed point relevant for various superconducting geometries.

Contribution

It extends previous work by identifying an infrared-stable fixed point in the model, independent of the number of compactified dimensions, applicable to different superconducting forms.

Findings

Identifies an infrared-stable fixed point in the model.

Fixed point is independent of the number of compactified dimensions.

Generalizes previous results for type-II superconducting films.

Abstract

We consider the Euclidean large-$N$ Ginzburg--Landau model in $D$ dimensions, $d$ ($d\leq D$) of them being compactified. For D=3, the system can be supposed to describe, in the cases of d=1, d=2, and d=3, respectively, a superconducting material in the form of a film, of an infinitely long wire having a rectangular cross-section and of a brick-shaped grain. We investigate the fixed-point structure of the model, in the presence of an external magnetic field. An infrared-stable fixed points is found, which is independent of the number of compactified dimensions. This generalizes previous work for type-II superconducting films