Irreversible Markov chain Monte Carlo algorithm for self-avoiding walk

We formulate an irreversible Markov chain Monte Carlo algorithm for the self-avoiding walk (SAW), which violates the detailed balance condition and satisfies the balance condition. Its performance improves significantly compared to that of the Berretti-Sokal algorithm, which is a variant of the Metropolis-Hastings method. The gained efficiency increases with spatial dimension (D), from approximately 1 0 times in 2D to approximately 4 0 times in 5D. We simulate the SAW on a 5D hyper-cubic lattice with periodic boundary conditions, for a linear system with a size up to L = 128, and confirm that as for the 5D Ising model, the finite-size scaling of the SAW is governed by renormalized exponents, nu* = 2/d and gamma/nu* = d/2. The critical point is determined, which is approximately 8 times more precise than the best available estimate.