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 4^4 to 12^4. 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.

revtex, 12 pages, 9 figures

References in corpus (3)

• Gauge-ball spectrum of the four-dimensional pure U(1) gauge theory
• Critical properties and monopoles in U(1) lattice gauge theory
• The Phase Diagram of the $U(2)\times U(2)$ Sigma Model

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• Density of states and Fisher's zeros in compact U(1) pure gauge theory
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• Simulations of Alice Electrodynamics on a Lattice
• Phase structure of U(1) lattice gauge theory with monopole term
• Finite Size Analysis of the U(1) Phase Transition using the World-sheet Formulation