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

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 2016, while for three-dimensional walks, it is 3--5 times faster.

The algorithms creating SAWs usually manipulate dif-ferent kinds of proposed moves, often referred to asatmospheres. 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.

Potential direct applications of the proposed algorithm are in increased efficiency in the numerical studies of finite-scaling and two-point functions of Ising model and n vector spin model.