High-statistics finite size scaling analysis of U(1) lattice gauge theory with a 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 ν is lattice-size dependent for volumes ranging from 4 4 to 12 4 . 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 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.

Simulations of Alice electrodynamics on a lattice

“…We note that in the pure Z 2 limit, the second term on the r.h.s. of equations (8) and (10) becomes zero and that c 4D and its three dimensional analogue c 3D follow from pure Z 2 gauge theory results as mentioned before. In fact, they are even known analytically [6].…”

Density of states and Fisher’s zeros in compactU(1)pure gauge theory

“…VI, we explained that for the data for L = 4, 6 and 8, the imaginary part of the lowest zeros scales like L −3.08 . It is possible that as the volume increases, the approach of the real axis "rolls" toward the L −4 scaling L Reβ ∆Re/2 Imβ ∆Im/2 10 1.00947 2e-5 0.001478 2e-6 12 1.01027 2e-5 0.000795 2e-6 14 1.01064 2e-5 0.000449 8e-6 20 1.01101 1e-5 0.000119 1e-6 expected for a first order transition [30]. We now discuss the scaling of the zeros using the lower statistics data for the larger volumes given in Table VIII.…”

“…At finite volume, it is easy to locate the value of β, denoted β S hereafter, where the two peaks of f (s) − β S s have equal height. Other pseudocritical β have been defined in the literature [30,[48][49][50]. The accuracy of the determination of β S depends on the smoothness of the distribution and the size of the error bars.…”

“…In addition, finite size scaling, at relatively small volumes seems consistent with a second order phase transition with an exponent ν ≃ 0.35 − 0.40. On the other hand, a possible scenario [30] is that as the volume increases, ν slowly "rolls" towards the first-order value ν = 1/D = 0.25. In the more recent literature [31][32][33][34], the idea that the transition is first order is favored.…”

Multicanonical hybrid Monte Carlo algorithm: Boosting simulations of compact QED

“…However, the latent heat is found to decrease with the lattice size and the critical exponent ν is neither 0.25 (first order) nor 0.5 (trivially second-order) [18]. These facts allow for two possible propositions:…”