Nonreversible Markov chain Monte Carlo algorithm for efficient generation of Self-Avoiding Walks

TL;DR

This paper presents a new nonreversible Markov chain Monte Carlo algorithm that efficiently generates self-avoiding walks, outperforming previous methods especially in three dimensions, by allowing flexible elementary moves.

Contribution

The paper introduces a novel nonreversible MCMC algorithm for self-avoiding walks that improves efficiency and speed over existing algorithms, particularly in three-dimensional cases.

Findings

Slightly better performance in 2D compared to previous algorithms.

3-5 times faster in 3D than existing methods.

Allows three types of elementary moves: shorten, extend, or alter conformation.

Abstract

We introduce an efficient nonreversible Markov chain Monte Carlo algorithm to generate self-avoiding walks with a variable endpoint. In two dimensions, the new algorithm slightly outperforms the two-move nonreversible Berretti-Sokal algorithm introduced by H.~Hu, X.~Chen, and Y.~Deng in \cite{old}, while for three-dimensional walks, it is 3--5 times faster. The new algorithm introduces nonreversible Markov chains that obey global balance and allows for three types of elementary moves on the existing self-avoiding walk: shorten, extend or alter conformation without changing the walk's length.