  The dependence of the Landau gauge two point gluon and ghost correlation
functions on the lattice spacing and on the physical volume are investigated
for pure SU(3) Yang-Mills theory in four dimensions using lattice simulations.
We present data from very large lattices up to $128^4$ and for two lattice
spacings $0.10$ fm and $0.06$ fm corresponding to volumes of $\sim$ (13 fm)$^4$
and $\sim$ (8 fm)$^4$, respectively. Our results show that, for sufficiently
large physical volumes, both propagators have a mild dependence on the lattice
volume. On the other hand, the gluon and ghost propagators change with the
lattice spacing $a$ in the infrared region, with the gluon propagator having a
stronger dependence on $a$ compared to the ghost propagator. In what concerns
the strong coupling constant $\alpha_s (p^2)$, as defined from gluon and ghost
two point functions, the simulations show a sizeable dependence on the lattice
spacing for the infrared region and for momenta up to $\sim 1$ GeV.
