Masses and Phase Structure in the Ginzburg-Landau Model

We study numerically the phase structure of the Ginzburg-Landau model, with particular emphasis on mass measurements and the infinite volume and continuum limits. There is no local gauge invariant order parameter, but we find that there is a phase transition characterized by a vanishing photon mass. For type I superconductors the transition is of 1st order. For type II 1st order is excluded by susceptibility analysis, and the data are even incompatible with 2nd order for a finite - but very small - lattice spacing: the scalar mass dips at T_c but remains non-zero for V\to\infty.