  The three-dimensional lattice Higgs model with compact U(1) gauge symmetry
and unit charge is investigated by means of Monte Carlo simulations. The full
model with fluctuating Higgs amplitude is simulated, and both energy as well as
topological observables are measured. The data show a Higgs and a confined
phase separated by a well-defined phase boundary, which is argued to be caused
by proliferating vortices. For fixed gauge coupling, the phase boundary
consists of a line of first-order phase transitions at small Higgs
self-coupling, ending at a critical point. The phase boundary then continues as
a Kertesz line across which thermodynamic quantities are nonsingular. Symmetry
arguments are given to support these findings.
