  We investigate the properties of hot and/or dense matter in QCD-like theories
with quarks in a (pseudo)real representation of the gauge group using the
Nambu-Jona-Lasinio model. The gauge dynamics is modeled using a simple lattice
spin model with nearest-neighbor interactions. We first keep our discussion as
general as possible, and only later focus on theories with adjoint quarks of
two or three colors. Calculating the phase diagram in the plane of temperature
and quark chemical potential, it is qualitatively confirmed that the critical
temperature of the chiral phase transition is much higher than the
deconfinement transition temperature. At a chemical potential equal to half of
the diquark mass in the vacuum, a diquark Bose-Einstein condensation (BEC)
phase transition occurs. In the two-color case, a Ginzburg-Landau expansion is
used to study the tetracritical behavior around the intersection point of the
deconfinement and BEC transition lines, which are both of second order. We
obtain a compact expression for the expectation value of the Polyakov loop in
an arbitrary representation of the gauge group (for any number of colors),
which allows us to study Casimir scaling at both nonzero temperature and
chemical potential.
