Physical Presentation of the Model—Critical Fields

Abstract

We begin by describing how the expression (1.1) for the Ginzburg-Landau functional is deduced from the expression (2.1) below, more commonly found in the physics literature. We will also give a nonrigorous introduction to critical fields in ℝ², in the spirit of Abrikosov, and draw a corresponding phase diagram in the (ε, h_ex) plane, i.e., qualitatively describe minimizers of the Ginzburg-Landau energy for different values of ε and h_ex, emphasizing the role of the vortices. Three areas of the parameter plane will be found: the normal, superconducting and mixed states, separated by what are usually called critical lines.