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

Monte Carlo study of four-dimensional self-avoiding walks of up to one billion steps