Phase structure, magnetic monopoles, and vortices in the lattice Abelian Higgs model

We present Monte Carlo calculations of lattice Abelian Higgs models in four dimensions and with charges of the Higgs particles equal to q=1, 2, and 6. The phase transitions are studied in the plane of the two coupling constants considering separately average plaquette and average link expectation values. The density of topological excitations is studied. In the confinement phase we find finite densities of magnetic-monopole currents, electric currents, and vortex currents. The magnetic-monopole currents vanish exponentially in the Coulomb phase. The density of electric currents and vortex currents is finite in the Coulomb phase and vanishes exponentially in the Higgs phase.