  The Quantum Chromodynamics (QCD) phase structure has been studied using the
Polyakov-loop augmented quark-meson model (PQM) in the extended mean field
approximation (e-MFA) where the quark one-loop vacuum term is included.~When
the divergent vacuum term is regularized in the minimal subtraction scheme and
the curvature meson masses are used to fix the parameters,~the Polyakov
quark-meson model with the vacuum term (PQMVT) becomes inconsistent as the
curvature masses are determined by calculating the self energies at zero
momentum.~The above inconsistency is remedied by the on-shell parameter fixing
when the pion decay constant and the pole masses of the mesons are put into the
relation of the couplings and running mass parameter by using the on-shell and
the minimal subtraction renormalization scheme.~Combining the modified chiral
effective potential of the on-shell renormalized quark-meson model (RQM) with
the Polyakov-loop potential that mimics the physics of the
confinement-deconfinement transition,~we get the renormalized Polyakov
quark-meson (RPQM) model.~The phase diagrams and the thermodynamics details for
the PQM, PQMVT and RPQM model, have been computed and compared for different
forms of the Polyakov-loop potentials with and without the quark
back-reaction.~The results have also been compared with the available lattice
QCD data.~The so called quarkyonic phase region in the phase diagram, where the
chiral symmetry is restored but the quarks and anti-quarks are still
confined,~gets reduced by the quark back-reaction in the unquenched
Polyakov-loop potential.~It altogether disappears for the chemical potential
dependent parameter $T_{0} \equiv T_{0} (\mu)$ in the Log or the PolyLog-glue
form of the Polyakov-loop potential in the RPQM model.
