A worm algorithm for the fully-packed loop model

Details A worm algorithm for the fully-packed loop model A worm algorithm for the fully-packed loop model

2008-11-13

arxiv.org/abs/0811.2042v2

Nuclear Physics B 814, 461-484 (2009)

Physics

Condensed Matter

Statistical Mechanics

31 pages, 10 figures. Several new figures added, and some minor typos corrected. Uses the following latex packages: algorithm.

Scientific paper

10.1016/j.nuclphysb.2009.01.007

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.

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