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

## TL;DR

This paper introduces a scale-free Monte Carlo method using a pivot algorithm to accurately estimate the critical exponent γ for three-dimensional self-avoiding walks by sampling walk pairs efficiently.

## Contribution

The paper develops a scale-free pivot algorithm for self-avoiding walks and applies it to precisely compute the critical exponent γ.

## Key findings

- Estimated γ as 1.15695300(95) with high precision
- Demonstrated efficiency of the scale-free Monte Carlo approach
- Provided insights into the properties of the Markov chain used

## 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 $1.15695300(95)$.