  Using the effective potential approach for composite operators, we have
formulated a general method how to calculate the truly nonperturbative vacuum
energy density in the axial gauge QCD quantum models of its ground state. It is
defined as integrated out the truly nonperturbative part of the full gluon
propagator over the deep infrared region (soft momentum region). The nontrivial
minimization procedure makes it possible to determine the value of the soft
cutoff in terms of the corresponding nonperturbative scale parameter which is
inevitably presented in any nonperturbative model for the full gluon
propagator. If the chosen Ansatz for the full gluon propagator is a realistic
one, then our method uniquely determines the truly vacuum energy density, which
is always finite, automatically negative and it has no imaginary part (stable
vacuum). We illustrate it by considering the Abelian Higgs model of dual QCD
ground state. We have explicitly shown that the vacuum of this model without
string contributions is unstable against quantum corrections.
