Abstract
We address the question of the order of the deconfinement phase transition of four dimensional U(1) lattice gauge theory. Simulations of the Z -gauge theory dual to the Villain action on toroidal lattices up to lattice sizes of 28 4 give results consistent with both, a vanishing and a nonvanishing discontinuity in the thermodynamic limit. A decision on the order of the phase transition requires still larger lattice sizes.
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