Irreversible Markov chain Monte Carlo algorithm for self-avoiding walk
Date of Issue2017
School of Chemical and Biomedical Engineering
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, v* = 2/d and γ/v* = d/2. The critical point is determined, which is approximately 8 times more precise than the best available estimate.
Monte Carlo algorithms
Frontiers of Physics
© 2017 Higher Education Press and Springer-Verlag Berlin Heidelberg. This is the author created version of a work that has been peer reviewed and accepted for publication by Frontiers of Physics, Higher Education Press and Springer-Verlag Berlin Heidelberg. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: [http://dx.doi.org/10.1007/s11467-016-0646-6].