  We investigate the influence of the granularity of the lattice on the
potential between monopoles. Using the flux definition of monopoles we
introduce their centers of mass and are able to realize continuous shifts of
the monopole positions. We find periodic deviations from the $1/r$-behavior of
the monopole-antimonopole potential leading to local extrema. We suppose that
these meta-stabilities may influence the order of the phase transition in
compact QED.
