## Der Phasenübergang in der U(1)-Gittereichtheorie

### Derivate 443

1.26 MB in one file, last changed at 22.01.2018

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d080306.pdf | 22.01.2018 13:04:40 | 1.26 MB |

**In this work the phase**transition of 4d compact pure U(1) gauge theory with Wilson action is investigated. By means of a highly efficient parallel implementation of the multicanonical Hybrid Monte Carlo algorithm we simulate systems of lattice sizes up to 18

^{4}with (10

^{6}-10

^{7}) configurations respectively. The goal of the project is to produce unambiguous results as to the order of the U(1) phase transition.

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, beta* _{T}*
= 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 32^{4} at the
very transition coupling, beta* _{T}*.
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.