We study numerically the phase structure of the Ginzburg-Landau model,
with particular emphasis on mass measurements. There is no local gaug
e-invariant order parameter, but we find that there is a phase transit
ion characterized by a vanishing photon mass. For type-I superconducto
rs the transition is of first order. For type-II, a first-order transi
tion is excluded by susceptibility analysis, but the photon correlatio
n length is compatible with second-order critical behavior with nu sim
ilar to 1/2. The scalar mass, in contrast, does not show clear critica
l behavior in the type-II regime for V-->infinity, contrary to the con
ventional picture.