Abstract
The author considers the lattice Abelian Higgs model with frozen radial degrees of freedom using the mean-field approximation with one-loop corrections. In the weak-coupling region the behaviour of the frequencies arising in the expansion of the action allows the Higgs and Coulomb phases to be distinguished. Analytical results are presented for all phase transition lines. The phase structure obtained is in qualitative agreement with Monte Carlo calculations for Higgs charges q=1, 2 and 6.
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