  Some interesting nonperturbative properties of the strongly coupled 4D
compact U(1) lattice gauge theories, both without and with matter fields, are
pointed out. We demonstrate that the pure gauge theory has a non-Gaussian fixed
point with $\nu = 0.365(8)$ at the second order confinement-Coulomb phase
transition. Thus a non-asymptotic free and nontrivial continuum limit of this
theory, and of its various dual equivalents, in particular of a special case of
the effective string theory, can be constructed. Including a scalar matter
field (compact scalar QED), we confirm the Gaussian behavior at the endpoint of
the Higgs phase transition line. In the theory with both scalar and fermion
matter fields, we demonstrate the existence of a tricritical point. Here, the
chiral symmetry is broken, and the mass of unconfined composite fermions is
generated dynamically. Appart from the Goldstone bosons, the spectrum contains
also a massive scalar. This resembles the Higgs-Yukawa sector of the SM, albeit
of dynamical origin, like the Nambu--Jona-Lasinio model. However, the scaling
behavior is different from that in the NJL model and the nonperturbative
renormalizability might thus be possible.
