Characterization of phases and boundary effects in U(1) gauge theory

We show that the two phases of the 4-dimensional compact U(1) lattice gauge theory are characterized by the existence or absence of an infinite current network, defining “infinite” on a finite lattice in a manner appropriate to the chosen boundary conditions. In addition for open and fixed boundary conditions we demonstrate the effects of inhomogeneities and provide examples of the reappearance of an energy gap.