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The dependence of the Landau gauge two point gluon and ghost correlationfunctions on the lattice spacing and on the physical volume are investigatedfor 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 latticespacings $0.10$ fm and $0.06$ fm corresponding to volumes of $\sim$ (13 fm)$^4$and $\sim$ (8 fm)$^4$, respectively. Our results show that, for sufficientlylarge physical volumes, both propagators have a mild dependence on the latticevolume. On the other hand, the gluon and ghost propagators change with thelattice spacing $a$ in the infrared region, with the gluon propagator having astronger dependence on $a$ compared to the ghost propagator. In what concernsthe strong coupling constant $\alpha_s (p^2)$, as defined from gluon and ghosttwo point functions, the simulations show a sizeable dependence on the latticespacing for the infrared region and for momenta up to $\sim 1$ GeV.

Lattice Gluon and Ghost Propagators, and the Strong Coupling in Pure SU(3) Yang-Mills Theory: Finite Lattice Spacing and Volume Effects