The ground state energy of the three dimensional Ginzburg-Landau model in the mixed phase

TL;DR

This paper estimates the leading order ground state energy of the 3D Ginzburg-Landau model in the mixed phase, where the magnetic field strength is between the first and second critical fields, as the Ginzburg-Landau parameter grows large.

Contribution

It provides a precise asymptotic estimate of the ground state energy in the mixed phase for the 3D Ginzburg-Landau model with large Ginzburg-Landau parameter.

Findings

Asymptotic estimate of ground state energy in the mixed phase

Analysis valid for large Ginzburg-Landau parameter

Applicable to three-dimensional bounded smooth domains

Abstract

We consider the Ginzburg-Landau functional defined over a bounded and smooth three dimensional domain. Supposing that the strength of the applied magnetic field varies between the first and second critical fields, in such a way that $H_{C_1}\ll H\ll H_{C_2}$, we estimate the ground state energy to leading order as the Ginzburg-Landau parameter tends to infinity.