  The hadron-quark/gluon phase transition is studied in the two-phase model. As
a further study of our previous work, both the isoscalar and isovector vector
interactions are included in the Polyakov loop modified Nambu--Jona-Lasinio
model (PNJL) for the quark phase. The relevance of the exchange (Fock) terms is
stressed and suitably accounted for. The calculation shows that the isovector
vector interaction delays the phase transition to higher densities and the
range of the mixed phase correspondingly shrinks. Meanwhile the asymmetry
parameter of quark matter in the mixed phase decreases with the strengthening
of this interaction channel. This leads to some possible observation signals
being weakened, although still present. We show that these can be rather
general effects of a repulsion in the quark phase due to the symmetry energy.
This is also confirmed by a simpler calculation with the MIT--Bag model.
However, the asymmetry parameter of quark matter is slightly enhanced with the
inclusion of the isoscalar vector interaction, but the phase transition will be
moved to higher densities. The largest uncertainty on the phase transition lies
in the undetermined coupling constants of the vector interactions. In this
respect new data on the mixed phase obtained from Heavy Ion Collisions at
Intermediate Energies appear very important.
