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We describe the results of a systematic high-statistics Monte-Carlo study offinite-size effects at the phase transition of compact U(1) lattice gaugetheory with Wilson action on a hypercubic lattice with periodic boundaryconditions. We find unambiguously that the critical exponent nu is lattice-sizedependent for volumes ranging from 4^4 to 12^4. Asymptotic scaling formulasyield values decreasing from nu(L >= 4) = 0.33 to nu(L >= 9) = 0.29. Ourstatistics are sufficient to allow the study of different phenomenologicalscenarios for the corrections to asymptotic scaling. We find evidence thatcorrections to a first-order transition with nu=0.25 provide the most accuratedescription of the data. However the corrections do not follow always theexpected first-order pattern of a series expansion in the inverse latticevolume V^{-1}. Reaching the asymptotic regime will require lattice sizesgreater than L=12. Our conclusions are supported by the study of many cumulantswhich all yield consistent results after proper interpretation.Comment: revtex, 12 pages, 9 figure

High-statistics finite size scaling analysis of U(1) lattice gauge theory with a Wilson action