  Finite-size effects in the free energy density for Abelian (anti-)self-dual
gluon field are investigated within $SU(3)$ gluodynamics. In particular, the
role of gluon quasi-zero modes is studied. The effective potential is
calculated within the framework of zeta function regularization for finite
spherical four-dimensional region of radius $R$ in Euclidean space-time. In
order to obtain the correct strong-field behavior of the effective potential
which is determined by the asymptotic freedom, the quasi-zero gluon modes have
to be treated beyond one-loop approximation in line with the argumentaion of
Leutwyler. Conditions for appearance of the global minimum of the free energy
density at finite nonzero values of both field strength and region size are
discussed.
