We present evidence that the existence of a first order phase transition in
compact U(1) with Wilson action is not related to monopole loops wrapping
around the toroidal lattice, as has been previously suggested. Our analysis is
based on the suppression of such loops by `soft boundary conditions' that
correspond to an infinitely large chemical potential for the monopoles on the
boundary, during the updating process. It is observed that the double peak
structure characteristic for the first order phase transition reappears at
sufficiently large lattice sizes and separations from the lattice boundary.Comment: 8 pages, (color) ps-figures available via anonymous ftp at
ftp://wpts0.physik.uni-wuppertal.de/pub/monopoles/figures.u
