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

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Abstract
We describe the results of a systematic high-statistics Monte Carlo study of finite-size effects at the phase transition of compact U(1) lattice gauge theory with a Wilson action on a hypercubic lattice with periodic boundary conditions. We find unambiguously that the critical exponent ν is lattice-size dependent for volumes ranging from 44 to 124. Asymptotic scaling formulas yield values decreasing from ν(L>~4)≈0.33 to ν(L>~9)≈0.29. Our statistics are sufficient to allow the study of different phenomenological scenarios for the corrections to asymptotic scaling. We find evidence that corrections to a first-order transition with ν=0.25 provide the most accurate description of the data. However the corrections do not always follow the expected first-order pattern of a series expansion in the inverse lattice volume V−1. Reaching the asymptotic regime will require lattice sizes greater than L=12. Our conclusions are supported by the study of many cumulants which all yield consistent results after proper interpretation.
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