  We investigate the phase diagram of the so-called
Polyakov--Nambu--Jona-Lasinio (PNJL) model at finite temperature and nonzero
chemical potential. The calculations are performed in the light and strange
quark sectors ($u$, $d$, $s$), which includes the 't Hooft instanton induced
interaction term that breaks the axial symmetry, and the quarks are coupled to
the (spatially constant) temporal background gauge field. On one hand, a
special attention is payed to the critical end point (CEP). The strength of the
flavor-mixing interaction alters the CEP location, since when it becomes weaker
the CEP moves to low temperatures and can even disappear. On the other hand, we
also explore the connection between QCD, a nonlocal Nambu--Jona-Lasinio type
model and the Landau gauge gluon propagator. Possible links between the
quenched gluon propagator and low energy hadronic phenomenology are
investigated.
