A worm algorithm for the fully-packed loop model
Abstract
We present a Markov-chain Monte Carlo algorithm of worm type that correctly simulates the fully-packed loop model on the honeycomb lattice, and we prove that it is ergodic and has uniform stationary distribution. The fully-packed loop model on the honeycomb lattice is equivalent to the zero-temperature triangular-lattice antiferromagnetic Ising model, which is fully frustrated and notoriously difficult to simulate. We test this worm algorithm numerically and estimate the dynamic exponent z = 0.515(8). We also measure several static quantities of interest, including loop-length and face-size moments. It appears numerically that the face-size moments are governed by the magnetic dimension for percolation.
Cite
@article{arxiv.0811.2042,
title = {A worm algorithm for the fully-packed loop model},
author = {Wei Zhang and Timothy M. Garoni and Youjin Deng},
journal= {arXiv preprint arXiv:0811.2042},
year = {2009}
}
Comments
31 pages, 10 figures. Several new figures added, and some minor typos corrected. Uses the following latex packages: algorithm.sty, algorithmic.sty, elsart-num.bst, elsart1p.cls, elsart.cls