Accurate Estimate of the Critical Exponent ν for Self-Avoiding Walks via a Fast Implementation of the Pivot Algorithm

We introduce a fast implementation of the pivot algorithm for self-avoiding walks, which we use to obtain large samples of walks on the cubic lattice of up to 33 x 10(6) steps. Consequently the critical exponent nu for three-dimensional self-avoiding walks is determined to great accuracy; the final estimate is nu = 0.587 597(7). The method can be adapted to other models of polymers with short-range interactions, on the lattice or in the continuum.