High-statistics finite size scaling analysis of U(1) lattice gauge theory with Wilson action
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 Wilson action on a hypercubic lattice with periodic boundary conditions. We find unambiguously that the critical exponent nu is lattice-size dependent for volumes ranging from 44 to 124. Asymptotic scaling formulas yield values decreasing from nu(L >= 4) = 0.33 to nu(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 nu=0.25 provide the most accurate description of the data. However the corrections do not follow always 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.
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.