Abstract
Using the 1-loop reduced 3D action of the Abelian Higgs-model we discuss the order of its finite temperature phase transition. A two-variable saddle point approximation is proposed for the evaluation of the effective potential. The strength of the first order case scales like \sim e^{3-6}. Analytic asymptotic weak coupling and numerical small coupling solutions are compared with special emphasis on the cancellation of divergences. (Figures are not included, can be sent upon request from jako@hercules.elte.hu .)
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