Chiral phase transition of QCD at finite temperature and density from the Schwinger-Dyson equation

We study the chiral phase transition of QCD at finite temperature and density by numerically solving the 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 the Pagels-Stokar formula. The 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 metastable 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.