  We present results concerning the non-perturbative evaluation of the
renormalisation constant for the quark field, $Z_q$, from lattice simulations
with twisted mass quarks and three values of the lattice spacing. We use the
RI'-MOM scheme. $Z_q$ has very large lattice spacing artefacts; it is
considered here as a test bed to elaborate accurate methods which will be used
for other renormalisation constants. We recall and develop the non-perturbative
correction methods and propose tools to test the quality of the correction.
These tests are also applied to the perturbative correction method. We check
that the lattice spacing artefacts scale indeed as $a^2p^2$. We then study the
running of $Z_q$ with particular attention to the non-perturbative effects,
presumably dominated by the dimension-two gluon condensate $\VEV{A^2}$ in
Landau gauge. We show indeed that this effect is present, and not small. We
check its scaling in physical units confirming that it is a continuum effect.
It gives a $\sim 4%$ contribution at 2 GeV. Different variants are used in
order to test the reliability of our result and estimate the systematic
uncertainties. Finally combining all our results and using the known Wilson
coefficient of $\VEV{A^2}$ we find $g^2(\mu^2) \VEV{A^2}_{\mu^2\; CM} =
  2.01(11)(^{+0.61}_{- 0.73}) \;\mathrm {GeV}^2$ at $\mu=10\, \mathrm{GeV}$, in
fair agreement within uncertainties with the value indepently extracted from
the strong coupling constant.
