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Following our earlier investigations we examine the quantum-classical windingnumber transition in the Abelian-Higgs system. It is demonstrated that thesphaleron transition in this system is of the smooth second order type in thefull range of parameter space. Comparison of the action of classical vorticeswith that of the sphaleron supports our finding.Comment: final version, to appear in J. Phys.

Winding number transitions at finite temperature in thed= 2 Abelian-Higgs model