Compact Lattice QED and the Coulomb Potential
  The potential energy of a static charge distribution on a lattice is rigorously computed in the standard compact quantum electrodynamic model. The method used follows closely that of Weyl for ordinary quantum electrodynamics in continuous space-time. The potential energy of the static charge distribution is independent of temperature and can be calculated from the lattice version of Poisson's equation. It is the usual Coulomb potential. 
Y.N. Srivstava, A. Widom, M.H. Friedman, O.Panella