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Using a one-loop renormalization group improvement for the effectivepotential in the Higgs model of electrodynamics with electrically andmagnetically charged scalar fields, we argue for the existence of a triple(critical) point in the phase diagram ($\lambda_{run}, g_{run}^4$), where$\lambda_{run}$ is the renormalised running selfinteraction constant of theHiggs scalar monopoles and $g_{run}$ is their running magnetic charge. Thistriple point is a boundary point of three first-order phase transitions in thedual sector of the Higgs scalar electrodynamics: The "Coulomb" and twoconfinement phases meet together at this critical point. Considering thearguments for the one-loop approximation validity in the region of parametersaround the triple point A we have obtained the following triple point values ofthe running couplings: $(\lambda_{(A)}, g^2_{(A)})\approx(-13.4; 18.6)$, whichare independent of the electric charge influence and two--loop corrections to$g^2_{run}$ with high accuracy of deviations. At the triple point the mass ofmonopoles is equal to zero. The corresponding critical value of the electricfine structure constant turns out to be $\alpha_{crit} =\pi/g^2_{(A)}\approx{0.17}$ by the Dirac relation. This value is close to the$\alpha_{crit}^{lat}\approx{0.20\pm 0.015}$, which in a U(1) lattice gaugetheory corresponds to the phase transition between the "Coulomb" andconfinement phases. In our theory for $\alpha \ge \alpha_{crit}$ there are twophases for the confinement of the electrically charged particles. The resultsof the present paper are very encouraging for the Anti--grand unificationtheory which was developed previously as a realistic alternative to SUSY GUTs.The paper is also devoted to the discussion of this problem.Comment: 29 pages, 3 figures, late

PHASE TRANSITION IN THE HIGGS MODEL OF SCALAR FIELDS WITH ELECTRIC AND MAGNETIC CHARGES