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 $\sim (13\mathrm{fm}{)}^4$ and $\sim (8\mathrm{fm}{)}^4$, 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 $\sim 1\mathrm{GeV}$.

• Received 3 May 2016

DOI:https://doi.org/10.1103/PhysRevD.94.014502