The Ginzburg-Landau functional with vanishing magnetic field

TL;DR

This paper analyzes the Ginzburg-Landau functional with a vanishing magnetic field in 2D, deriving energy asymptotics for large parameters and revealing energy concentration near the magnetic field's zero set.

Contribution

It provides new asymptotic results for the Ginzburg-Landau functional with vanishing magnetic field, extending previous work to this specific regime.

Findings

Energy concentrates near the zero set of the magnetic field.

Asymptotic energy estimates valid for large Ginzburg-Landau parameter.

Completes previous results by analyzing the vanishing magnetic field case.

Abstract

We study the infimum of the Ginzburg-Landau functional in the case of a vanishing external magnetic field in a two dimensional simply connected domain. We obtain an energy asymptotics which is valid when the Ginzburg-Landau parameter is large and the strength of the external field is comparable with the third critical field. Compared with the known results when the external magnetic field does not vanish, we show in this regime a concentration of the energy near the zero set of the external magnetic field. Our results complete former results obtained by K. Attar and X-B. Pan--K-H.~Kwek.