Kertész line in the three-dimensional compact U(1) lattice Higgs model.

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 Kertész line across which thermodynamic quantities are non-singular. Symmetry arguments are given to support these findings.