### Abstract

We present a Markov-chain Monte Carlo algorithm of worm type that correctly simulates the O(n) loop model on any (finite and connected) bipartite cubic graph, for any real n>0, and any edge weight, including the fully-packed limit of infinite edge weight. Furthermore, we prove rigorously that the algorithm is ergodic and has the correct stationary distribution. We emphasize that by using known exact mappings when n=2, this algorithm can be used to simulate a number of zero-temperature Potts antiferromagnets for which the Wang-Swendsen-Kotecky cluster algorithm is non-ergodic, including the 3-state model on the kagome-lattice and the 4-state model on the triangular-lattice. We then use this worm algorithm to perform a systematic study of the honeycomb-lattice loop model as a function of n2 is also considered, and we confirm the existence of a phase transition in the 3-state Potts universality class that was recently observed via numerical transfer matrix calculations

Original language | English |
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Pages (from-to) | 283 - 315 |

Number of pages | 33 |

Journal | Nuclear Physics B |

Volume | 846 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2011 |

Externally published | Yes |

## Cite this

Liu, Q., Deng, Y., & Garoni, T. (2011). Worm Monte Carlo study of the honeycomb-lattice loop model.

*Nuclear Physics B*,*846*(2), 283 - 315. https://doi.org/10.1016/j.nuclphysb.2011.01.003