Worm Monte Carlo study of the honeycomb-lattice loop model

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• 作者：Qingquan Liu^a ; ^{liuqq@mail.ustc.edu.cn} ; Youjin Deng^a ; ^{yjdeng@ustc.edu.cn} ; Timothy M. Garoni^b ; ^{t.garoni@ms.unimelb.edu.au}
• 关键词：Monte Carlo ; Worm algorithm ; Loop model
• 刊名：Nuclear Physics B
• 出版年：2011
• 出版时间：11 May 2011
• 年：2011
• 卷：846
• 期：2
• 页码：283-315
• 全文大小：535 K

文摘

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–Kotecký 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, on the critical line and in the densely-packed and fully-packed phases. By comparing our numerical results with Coulomb gas theory, we identify a set of exact expressions for scaling exponents governing some fundamental geometric and dynamic observables. In particular, we show that for all n2, the scaling of a certain return time in the worm dynamics is governed by the magnetic dimension of the loop model, thus providing a concrete dynamical interpretation of this exponent. The case n>2 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.