easing lattice volume $V$. We have performed a fit as a function of $1/V$ and have seen that the large volume $\beta=3.92$ lattice gives results which are very close to the infinite volume limit. In Fig. \[fig:pert\_vs\_latt\] we plot $D(q^2)$ in the intermediate and ultraviolet regime and compare with the three-loop perturbative QCD form. We see that the above $q\sim 2$ GeV the agreement is excellent, but that below this momentum scale nonperturbative effects are becoming apparent.

Quark Propagator
================

The Landau gauge quark propagator results summarized here have been presented and discussed in more detail elsewhere.[@quark_prop] All ${\cal O}(a)$ errors in the fermion action can be removed by adding appropriate terms to the Lagrangian[@Luscher:1996sc; @Dawson:1997gp]. It is then usual to perform appropriate field transformations to improve the quark operators as well.[@Heatlie:1991kg]

(14,7) (0,0)

(7,7)(-0.9,-0.4)[[ ]{}]{}

(7,0)

(7,7)(-0.9,-0.4)[[ ]{}]{}

In the continuum, the quark propagator has the following general form, $$S(p) = \frac{1}{i{\not\!p}A^c(p) + B^c(p)} \equiv
\frac{Z^c(p)}{i{\not\!p}+M^c(p)}.$$ We expect the lattice quark propagator to have a similar form, but with ${\not\!k}$ replacing ${\not\!p}$: $$S(p) = \frac{Z(p)}{i{\not\!k}+ M(p)}$$ where $k$ is a new ‘lattice momentum’, $k_\mu = \frac{1}{a}\sin(\hat p_\mu a)$. We do not have sufficient space here to describe the hybrid tree-level correction that was used for the quark propagator results presented here, but a detailed description has recently been given.[@quark_prop] We again use the cylinder cut to further reduce hypercubic discretization artefacts. As for the gluon propagator the results for $Z(p)$ are for the bare quantity only and contain an overall renormalization constant $Z_2(\mu,a)$. In Fig. \[fig:z\_np\_compare\] the vertical scales have been adjusted so that the two sets of results are renormalized and hence coincide at 2.1 GeV. In this figure we see the charactreistic dip in the infrared for $Z(p)$,