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\begin{document}
{\noindent\LARGE{\bf Larisa Laperashvili}\\[1cm]
\noindent\bf{Multiple point criticality principle and phase transition
in regularized gauge theories with matter}}\\
Multiple Point Criticality Principle (MPCP) is an important idea of the
Anti - Grand Unification Theory (AGUT), according to which the unification
point is absent up to the Planck energy scale $M_{Pl} = 1.22\times
10^{19}\;GeV$ where the multiple critical point (MCP) of the fundamental
gauge theory exists. MCP is a special point in a phase diagram for the
regularized gauge theory where all (or at least maximum) number of phases
meet. The aim of this work is to investigate quantum electrodynamics with
monopoles for a phase transistion and calculate a critical coupling
constant at the phase border between "Coulomb" and "confined" phases,
asuming the existence of scalar monopoles (real ones or artifacts of
regularized theory). The technology is to consider ratios of the vacuum
diagrams and seek to estimate how the vacuum diagrams and tracelogs
for the partition function can ballance between the two phases giving
the critical coupling constant. The main purpose was to estimate the
degree of variation of the first order phase transition couplings under
the variation of the ultraviolet cut off. The result for ${\alpha}_{crit}$
obtained is ${\alpha}_{crit}\approx{0.23}$, in correspondence with
Monte Carlo simulation result on lattice (${\alpha}_{crit}\approx{0.20}$)
and with a regularized gauge theory using a nonlocal Wilson loop action
of radii $R\ge{a}\sim 1/M_{Pl} ({\alpha}_{crit}\approx{0.204})$. Such
an investigation confirms the "universality" (regularization independence)
of critical coupling constants which is needed for the fine structure
predictions claimed from MPCP and AGUT.
\end{document}