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We propose a method to compute the effective potential of QCD from gapequations by introducing the homotopy transformation between solutions of theequation of motion. Via this method, the effective potential can be obtainedbeyond the bare vertex approximation, which then generalizes the Cornwall,Jackiw and Tomboulis (CJT) effective potential for bilocal composite operators.Moreover, the extended effective potential is set to be a function of selfenergy instead of the composite operator, which is the key point to make thepotential bounded from below as for the auxiliary field (AF) Potential. We thenapply the effective potential in the coexistence region where there exists atleast two solutions, for instance, in vacuum with small current quark mass, andthe first order phase transition region in finite temperature and chemicalpotential, which provides the in-medium behavior of the latent heat and falsevacuum energy.

The effective potential of composite operator in the first order region of QCD phase transition