  We study numerically the phase structure of the Ginzburg-Landau model, with
particular emphasis on mass measurements. 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, but the
photon correlation length suggests 2nd order critical behaviour with \nu ~ 1/2.
The scalar mass, in contrast, does not show clear critical behaviour in the
type II regime for V \to \infty, contrary to the conventional picture.
