  An impact of the finite size effects on the vacuum free energy density of
full QCD with $N_{\rm f}$ massless flavors in the presence of homogeneous
(anti-)self-dual Abelian background gluon field is studied. The zero
temperature free energy density of the four-dimensional spherical domain is
computed as a function of the background field strength $B$ and domain radius
$R$. Calculation is performed in the one-loop approximation improved by
accounting for mixing of the quark and gluon quasi-zero modes with normal
modes, with the use of the $\zeta$-function regularization. It is indicated
that, under plausible assumption on the character of the mixing, the quantum
correction to the free energy density has a minimum as a function of $B$ and
$R$. Within the mean field approach to QCD vacuum based on domain wall network
representation of the mean field, an existence of the minimum may prevent
infinite growth of individual domain, thus protecting the vacuum from the
long-range ordering, and, hence, serving as the origin of disorder in the
statistical ensemble of domain wall networks, driven by the minimization of the
overall free energy of the dominant gauge field configurations.
