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We present a Markov-chain Monte Carlo algorithm of "worm"type that correctlysimulates the O(n) loop model on any (finite and connected) bipartite cubicgraph, for any real n>0, and any edge weight, including the fully-packed limitof infinite edge weight. Furthermore, we prove rigorously that the algorithm isergodic and has the correct stationary distribution. We emphasize that by usingknown exact mappings when n=2, this algorithm can be used to simulate a numberof zero-temperature Potts antiferromagnets for which the Wang-Swendsen-Koteckycluster algorithm is non-ergodic, including the 3-state model on thekagome-lattice and the 4-state model on the triangular-lattice. We then usethis worm algorithm to perform a systematic study of the honeycomb-lattice loopmodel as a function of n<2, on the critical line and in the densely-packed andfully-packed phases. By comparing our numerical results with Coulomb gastheory, we identify the exact scaling exponents governing some fundamentalgeometric and dynamic observables. In particular, we show that for all n<2, thescaling of a certain return time in the worm dynamics is governed by themagnetic dimension of the loop model, thus providing a concrete dynamicalinterpretation of this exponent. The case n>2 is also considered, and weconfirm the existence of a phase transition in the 3-state Potts universalityclass that was recently observed via numerical transfer matrix calculations.

Worm Monte Carlo study of the honeycomb-lattice loop model