  Using the effective potential approach for composite operators, we have
analytically evaluated the truly nonperturbative vacuum energy density as
obtained by using a model infrared finite gluon propagator which was suggested
by lattice simulations. The truly nonperturbative vacuum energy density is
defined as the truly nonperturbative part of the full gluon propagator
integrated over the deep infrared region (soft momentum region). With this
definition, it is a manifestly gauge invariant quantity. We have explicitly
shown that the corresponding effective potential has always an imaginary part
which means that the vacuum of this model is unstable. Thus this model cannot
have a true ground state.
