Infrared behavior of the gluon propagator on a large volume lattice

The first calculation of the gluon propagator using an $\mathcal{O}{(a}^2)$ improved action with the corresponding $\mathcal{O}{(a}^2)$ improved Landau gauge fixing condition is presented. The gluon propagator obtained from the improved action and improved Landau gauge condition is compared with earlier unimproved results on similar physical lattice volumes of ${3.2}^3\times 6.4{\mathrm{fm}}^4.$ We find agreement between the improved propagator calculated on a coarse lattice with lattice spacing $a=0.35\mathrm{}$ fm and the unimproved propagator calculated on a fine lattice with spacing $a=0.10\mathrm{}$ fm. This motivates us to calculate the gluon propagator on a coarse large-volume lattice ${5.6}^3\times 11.2{\mathrm{fm}}^4.$ The infrared behavior of previous studies is confirmed in this work. The gluon propagator is enhanced at intermediate momenta and suppressed at infrared momenta. Therefore the observed infrared suppression of the Landau gauge gluon propagator is not a finite volume effect.