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 = 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 = 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 z(exp)= 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.