Modified iterative versus Laplacian Landau gauge in compact U(1) theory

Compact U(1) theory in 4 dimensions is used to compare the modified iterative and the Laplacian fixing to lattice Landau gauge in a controlled setting, since in the Coulomb phase the lattice theory must reproduce the perturbative prediction. It turns out that on either side of the phase transition clear differences show up and in the Coulomb phase the ability to remove double Dirac sheets proves vital on a small lattice.