We study the Ginzburg-Landau energy of superconductors submitted to a possibly non-uniform magnetic eld, in the limit of a large Ginzburg-Landau parameter. We prove that the induced magnetic elds associated to minimizers of the energy-functional converge as ! +1 to the solution of a free-boundary problem. This free boundary-problem has a nontrivial solution only when the applied magnetic eld is...

The two dimensional lattice Ginzburg-Landau hamiltonian is simulated numerically for different values of the coherence length ξ in units of the lattice spacing a, a parameter which controls amplitude fluctuations. The phase diagram on the plane T − ξ is measured. Amplitude fluctuations change dramatically the nature of the phase transition: for values of ξ/a ≃ 1 , instead of the smooth Kosterli...