Fixed boundary conditions and phase transitions in pure gauge compact QED

We have simulated the pure gauge compact QED with fixed boundary conditions, on lattices from $6^4$ to ${16}^4$. We argue that a lattice with this fixed boundary imposition corresponds actually to a lattice with spherical topology. We have found the presence of a phase transition without any trace of discontinuity. Moreover, the specific heat and the Binder cumulant are qualitatively consistent with a second order phase transition. The implications of this observation on the nature of the compact lattice QED are discussed.