  We investigate non-perturbative features of a three-dimensional Abelian Higgs
model with singly- and doubly-charged scalar fields coupled to a single compact
Abelian gauge field. The model is pretending to describe various planar systems
of strongly correlated electrons such as high-Tc superconductivity in the
overdoped regime and exotic materials possessing excitations with
fractionalized quantum numbers. The complicated phase structure of the model is
studied thoroughly using numerical tools and analytical arguments. In the
three-dimensional space of coupling parameters we identify the Fermi liquid,
the spin gap, the superconductor and the strange metallic phases. The behavior
of three kinds of topological defects -- holon and spinon vortices and
monopoles - is explored in various phases. We also observe a new effect, the
strong enhancement of the phase transition strength reflected in a lower order
of the transition: at sufficiently strong gauge coupling the two second order
phase transitions -- corresponding to spinon-pair and holon condensation lines
- join partially in the phase diagram and become a first order phase transition
in that region. The last observation may have an analogue in Quantum
Chromodynamics at non-zero temperature and finite baryon density. We argue that
at sufficiently large baryon density the finite-temperature transition between
the (3-flavor paired) color superconducting phase and the quark-gluon plasma
phases should be much stronger compared with the transition between 2-flavor
paired and 3-flavor paired superconducting phases.
