  We compare different models for hadronic and quark phases of cold baryon-rich
matter in an attempt to find a deconfinement phase transition between them. For
the hadronic phase we consider Walecka-type mean-field models which describe
well the nuclear saturation properties. We also use the variational chain model
which takes into account correlation effects. For the quark phase we consider
the MIT bag model, the Nambu-Jona-Lasinio and the massive quasiparticle models.
By comparing pressure as a function of baryon chemical potential we find that
crossings of hadronic and quark branches are possible only in some exceptional
cases while for most realistic parameter sets these branches do not cross at
all. Moreover, the chiral phase transition, often discussed within the
framework of QCD motivated models, lies in the region where the quark phases
are unstable with respect to the hadronic phase. We discuss possible physical
consequences of these findings.
