Scale-free Monte Carlo method for calculating the critical exponent. of self-avoiding walks

摘要

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. for self-avoiding walks to unprecedented accuracy. Our final estimate for. is 1.156 953 00(95).