  We perform numerical studies of the running coupling constant alpha_R(p^2)
and of the gluon and ghost propagators for pure SU(2) lattice gauge theory in
the minimal Landau gauge. Different definitions of the gauge fields and
different gauge-fixing procedures are used respectively for gaining better
control over the approach to the continuum limit and for a better understanding
of Gribov-copy effects. We find that the ghost-ghost-gluon-vertex
renormalization constant is finite in the continuum limit, confirming earlier
results by all-order perturbation theory. In the low momentum regime, the gluon
form factor is suppressed while the ghost form factor is divergent.
Correspondingly, the ghost propagator diverges faster than 1/p^2 and the gluon
propagator appears to be finite. Precision data for the running coupling
alpha_R(p^2) are obtained. These data are consistent with an IR fixed point
given by lim_{p \to 0} alpha_R(p^2) = 5(1).
