Irreversible Markov chain Monte Carlo algorithm for the self-avoiding walk

We design an irreversible Markov chain Monte Carlo algorithm for the self-avoiding walk (SAW). It outperforms the Berretti-Sokal algorithm. The gained efficiency increases with the spatial dimension, from about 10 times in two dimensions to around 40 times in five dimensions. The algorithm violates the widely used detailed balance condition and satisfies the weaker balance condition. We employ the irreversible method to study the finite-size scaling of SAW above the upper critical dimension.