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

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