Worm Monte Carlo study of the honeycomb-lattice loop model

Qingquan Liu, Youjin Deng, Tim Garoni

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15 Citations (Scopus)


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 languageEnglish
Pages (from-to)283 - 315
Number of pages33
JournalNuclear Physics B
Issue number2
Publication statusPublished - 2011
Externally publishedYes

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