Accurate estimate of the critical exponent $\nu$ for self-avoiding walks via a fast implementation of the pivot algorithm

Abstract

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.

5 pages, 3 figures

References in corpus (4)

• Critical Exponents of the N-vector model
• Critical Exponents, Hyperscaling and Universal Amplitude Ratios for Two- and Three-Dimensional Self-Avoiding Walks
• Scaling of Self-Avoiding Walks and Self-Avoiding Trails in Three Dimensions
• Peculiar scaling of self-avoiding walk contacts

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