Scale-free Monte Carlo method for calculating the critical exponent $\gamma$ of self-avoiding walks

Abstract

We implement a scale-free version of the pivot algorithm and use it to sample pairs of three-dimensional self-avoiding walks, for the purpose of efficiently calculating an observable that corresponds to the probability that pairs of self-avoiding walks remain self-avoiding when they are concatenated. We study the properties of this Markov chain, and then use it to find the critical exponent $\gamma$ for self-avoiding walks to unprecedented accuracy. Our final estimate for $\gamma$ is $1.15695300(95)$.

11 pages

References in corpus (3)

• Accurate estimate of the critical exponent $\nu$ for self-avoiding walks via a fast implementation of the pivot algorithm
• High-precision estimate of the hydrodynamic radius for self-avoiding walks
• Unexpected relaxation dynamics of a self-avoiding polymer in cylindrical confinement

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