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 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 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, υ*= 2/d and γ/υ*= d/2. The critical point is determined, which is approximately 8 times more precise than the best available estimate.

Keywords

Monte Carlo algorithms / self-avoiding walk / irreversible / balance condition

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