  We present and discuss the results of a Monte-Carlo simulation of the phase
transition in pure compact U(1) lattice gauge theory with Wilson action on a
hypercubic lattice with periodic boundary conditions. The statistics are large
enough to make a thorough analysis of the size dependence of the gap. In
particular we find a non-zero latent heat in the infinite volume limit. We also
find that the critical exponents $\nu$ and $\alpha$ are consistent with the
hyperscaling relation but confirm that the critical behavior is different from
a conventional first-order transition.
