  We investigate both the chiral and deconfinement phase transitions of QCD
matter in a refined scheme of Dyson-Schwinger equations, which have been shown
to be successful in giving the meson mass spectrum and matching the interaction
with the results from ab initio computation. We verify the equivalence of the
chiral susceptibility criterion with different definitions for the
susceptibility and confirm that the chiral susceptibility criterion is
efficient to fix not only the chiral phase boundary but also the critical end
point (CEP), especially when one could not have the effective thermodynamical
potential. We propose a generalized Schwinger function criterion for the
confinement. We give the phase diagram of both phase transitions and show that
in the refined scheme the position of the CEP shifts to lower chemical
potential and higher temperature. Based on our calculation and previous results
of the chemical freeze out conditions, we propose that the CEP locates in the
states of the matter generated by the Au--Au collisions with
$\sqrt{s_{NN}^{}}=9\sim15$ GeV.
