  The phase transition "Coulomb-confinement" in the U(1) regularized gauge
theory is considered in the framework of dual Abelian Higgs model of scalar
monopoles (shortly: Higgs monopole model). The effective potential analogous to
the Coleman-Weinberg's one, improved by the renormalization group equation, is
constructed, using beta-functions in the two-loop approximation. The value of
QED critical fine structure constant was calculated: $\alpha_{crit}\approx
0.208$, in correspondence with lattice result: $\alpha_{crit}^{lat}\approx
0.20\pm 0.015$.
