  We study self-avoiding walks on the four-dimensional hypercubic lattice via
Monte Carlo simulations of walks with up to one billion steps. We study the
expected logarithmic corrections to scaling, and find convincing evidence in
support the scaling form predicted by the renormalization group, with an
estimate for the power of the logarithmic factor of 0.2516(14), which is
consistent with the predicted value of 1/4. We also characterize the behaviour
of the pivot algorithm for sampling four-dimensional self-avoiding walks, and
conjecture that the probability of a pivot move being successful for an
$N$-step walk is $O([ \log N ]^{-1/4})$.
