  We study the chiral phase transition of QCD at finite temperature and density
by numerically solving Schwinger-Dyson equation for the quark propagator with
the improved ladder approximation in the Landau gauge. Using the solution we
calculate a pion decay constant from a generalized version of Pagels-Stokar
formula. Chiral phase transition point is determined by analyzing an effective
potential for the quark propagator. We find solutions for which chiral symmetry
is broken while the value of the effective potential is larger than that for
the chiral symmetric vacuum. These solutions correspond to meta-stable states,
and the chiral symmetric vacuum is energetically favored. We present a phase
diagram on the general temperature--chemical potential plane, and show that
phase transitions are of first order in wide range.
