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 64 to 164. 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. © 1994.