The universal behavior of superconductors near the phase transition is described by the three-dimensional field theory of scalar quantum electrodynamics. We approximately solve the model with the help of nonperturbative flow equations. A first-or second-order phase transition is found depending on the relative strength of the scalar versus the gauge coupling. The region of a second-order phase transition is governed by a fixed point of the flow equations with associated critical exponents. We also give an approximate description of the tricritical behavior and briefly discuss the crossover relevant for the onset of scaling near the critical temperature. Final confirmation of a second-order transition for strong type-II superconductors requires further analysis with extended truncations of the flow equations.

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Non-perturbative exact flow equations describe the scale dependence of the effective average action. We present a numerical solution for an approximate form of the flow equation for the potential in a three-dimensional N -component scalar field theory. The critical behaviour, with associated critical exponents, can be inferred with good accuracy.

Article (Published Version) http://sro.sussex.ac.uk Freire, Filipe and Litim, Daniel F (2001) Charge crossover at the U(1) Higgs phase transition. Physical Review D, 64 (4). ISSN 1550-7998 This version is available from Sussex Research Online: http://sro.sussex.ac.uk/18989/ This document is made available in accordance with publisher policies and may differ from the published version or from the version of record. If you wish to cite this item you are advised to consult the publisher's version. Please see the URL above for details on accessing the published version. Copyright and reuse:Sussex Research Online is a digital repository of the research output of the University.Copyright and all moral rights to the version of the paper presented here belong to the individual author(s) and/or other copyright owners. To the extent reasonable and practicable, the material made available in SRO has been checked for eligibility before being made available.Copies of full text items generally can be reproduced, displayed or performed and given to third parties in any format or medium for personal research or study, educational, or not-for-profit purposes without prior permission or charge, provided that the authors, title and full bibliographic details are credited, a hyperlink and/or URL is given for the original metadata page and the content is not changed in any way. The type-I region of phase transitions at finite temperature of the U(1)-Higgs theory in 3ϩ1 dimensions is investigated in detail using a Wilsonian renormalization group. We consider, in particular, the quantitative effects induced through the crossover of the scale-dependent Abelian charge from the Gaussian to a nontrivial Abelian fixed point. As a result, the strength of the first-order phase transition is weakened. Analytical solutions to approximate flow equations are obtained, and all characteristics of the phase transition are discussed and compared to the results obtained from perturbation theory. In addition, we present a detailed quantitative study regarding the dependence of the physical observables on the coarse-graining scheme. This results in error bars for the regularization scheme ͑RS͒ dependence. We find quantitative evidence for an intimate link between the RS dependence and truncations of flow equations. Charge crossover at the U"1…-Higgs phase transition