Irreversible Markov chain Monte Carlo algorithm for self-avoiding walk
Abstract
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 the spatial dimension (D), from approximately 10 times in 2D to approximately 40 times in 5D. We simulate the SAW on a 5D hypercubic lattice with periodic boundary conditions, for a system with a linear 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 *=2/d and γ/*=d/2. The critical point is determined, which is approximately 8 times more precise than the best available estimate.