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 ${\nu }^{\ast }=2/d$ and $\gamma /{\nu }^{\ast }=d/2$. The critical point is determined, which is approximately $8$ times more precise than the best available estimate.

7 pages, 6 figures

References in corpus (3)

• 2D Melting: From Liquid-Hexatic Coexistence to Continuous Transitions
• Markov Chain Monte Carlo Method without Detailed Balance
• Finite-size scaling above the upper critical dimension

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• Unwrapped two-point functions on high-dimensional tori
• Lifted directed-worm algorithm
• Finite-Size Scaling of the High-Dimensional Ising Model in the Loop Representation
• Graphical Representations and Worm Algorithms for the O($N$) Spin Model