  We propose a method to compute the effective potential of QCD from gap
equations by introducing the homotopy transformation between solutions of the
equation of motion. Via this method, the effective potential can be obtained
beyond 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 self
energy instead of the composite operator, which is the key point to make the
potential bounded from below as for the auxiliary field (AF) Potential. We then
apply the effective potential in the coexistence region where there exists at
least two solutions, for instance, in vacuum with small current quark mass, and
the first order phase transition region in finite temperature and chemical
potential, which provides the in-medium behavior of the latent heat and false
vacuum energy.

High Energy Physics - Phenomenology;High Energy Physics - Theory