Topological excitations and Monte Carlo simulation of Abelian gauge theory

We study the phase structure of lattice electrodynamics in three and four dimensions using Monte Carlo simulation, with special emphasis on the topological excitations of the theory. We formulate an operational definition of a monopole and measure the density of monopoles as a function of coupling constant. In three dimensions and for strong coupling in four dimensions monopoles screen external magnetic fields. Below a critical coupling in four dimensions the external field penetrates into the bulk of the medium; this long-range correlation essentially shows that the lattice theory in weak coupling is characterized by a massless photon.