A worm algorithm for the fully-packed loop model

We present a Markov-chain Monte Carlo algorithm of worm   type that correctly simulates the fully-packed loop model with n=1n=1 on the honeycomb lattice, and we prove that it is ergodic and has uniform stationary distribution. The honeycomb-lattice fully-packed loop model with n=1n=1 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 zexp=0.515(8)zexp=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.