Irreversible Markov chain Monte Carlo algorithm for selfavoiding walk
Abstract
We formulate an irreversible Markov chain Monte Carlo algorithm for the selfavoiding walk (SAW), which violates the detailed balance condition and satisfies the balance condition. Its performance improves significantly compared to that of the BerrettiSokal algorithm, which is a variant of the MetropolisHastings 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 finitesize 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.
 Publication:

Frontiers of Physics
 Pub Date:
 February 2017
 DOI:
 10.1007/s1146701606466
 arXiv:
 arXiv:1602.01671
 Bibcode:
 2017FrPhy..12l0503H
 Keywords:

 Monte Carlo algorithms;
 selfavoiding walk;
 irreversible;
 balance condition;
 Condensed Matter  Statistical Mechanics;
 Physics  Computational Physics
 EPrint:
 7 pages, 6 figures