Accurate estimate of the critical exponent $\nu$ 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 $33\times {10}^6$ steps. Consequently the critical exponent $\nu$ for three-dimensional self-avoiding walks is determined to great accuracy; the final estimate is $\nu =0.587597(7)$. The method can be adapted to other models of polymers with short-range interactions, on the lattice or in the continuum.