Physical Presentation of the Model—Critical Fields
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, hex) plane, i.e., qualitatively describe minimizers of the Ginzburg-Landau energy for different values of ε and hex, 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.
KeywordsGauge Transformation Critical Field Hexagonal Lattice Critical Line Normal Solution
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