Coulomb law in the pure gauge U(1) theory on a lattice

We study the heavy charge potential in the Coulomb phase of pure gauge compact U(1) theory on the lattice. We calculate the static potential V{sub W}(T,{rvec R}) from Wilson loops on a 16{sup 3}{times}32 lattice and compare with the predictions of lattice perturbation theory. We investigate finite size effects and, in particular, the importance of non-Coulomb contributions to the potential. We also comment on the existence of a maximal coupling in the Coulomb phase of pure gauge U(1) theory. {copyright} {ital 1997} {ital The American Physical Society}