Der Phasenübergang in der U(1)-Gittereichtheorie
In a heuristic extension of the first order finite size scaling (FSS) theory of Borgs-Kotecky to U(1) gauge theory we investigate several cumulants of the plaquette energy. We find scaling to be consistent with a series expansion in terms of the reciprocal volume of the System 1/V. In particular the pseudocritical couplings beta(V) can be described by this ansatz with high precision and stability. We extract the infinite volume transition coupling, betaT = 1.0111331(21), and determine the asymmetry, log(X) = 3.21(10) where X denotes the relative weight of the coulomb phase over the confined phase in the infinite volume limit.
Since we cannot definitely discard the possibility of an asymptotic second order scaling that might show up on large lattice sizes, we investigate the latent heat by additional simulations of both metastable branches on lattice sizes up to 324 at the very transition coupling, betaT. The occurrence of a nonvanishing energy gap indicates a discontinuous phase transition. Futhermore its value is consistent with the gap obtained from FSS of the specific heat within the Borgs-Kotecky scheme.
An independent leading order perturbative lattice calculation confirms a first order scaling of the pseudocritical coupling as defined by the equilibrium of the free energies in both phases. The leading correction reveals an asymmetry of log(X) = 3.15(8) in striking agreement with the FSS result. Yet we are faced with deviations from the Borgs-Kotecky scheme in higher order corrections to asymptotic scaling and conclude that either the Borgs-Kotecky first order theory or lattice perturbation theory might exhibit only asymptotic convergence. This does however not affect the clear evidence of a discontinuous phase transition determined by the non vanishing infinite volume gap.