Critical loop gases and the worm algorithm

Janke, Wolfhard; Neuhaus, T.; Schakel, Adriaan M. J.

doi:10.1016/j.nuclphysb.2009.12.024

Cited by 12 publications

(8 citation statements)

References 38 publications

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“…of lengths (number of link-lines) |λ i |. In [17], inspired by percolation and random walk theory, the asymptotic scaling form…”

Section: Why An Improved Method?mentioning

confidence: 99%

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Simulating the all-order strong coupling expansion IV: CP(N−1) as a loop model

Wolff

2010

Nuclear Physics B

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We exactly reformulate the lattice CP(N − 1) spin model on a D dimensional torus as a loop model whose configurations correspond to the complete set of strong coupling graphs of the original system. A Monte Carlo algorithm is described and tested that samples the loop model with its configurations stored and manipulated as a linked list. Complete absence of critical slowing down and correspondingly small errors are found at D = 2 for several observables including the mass gap. Using two different standard lattice actions universality is demonstrated in a finite size scaling study. The topological charge is identified in the loop model but not yet investigated numerically.

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“…of lengths (number of link-lines) |λ i |. In [17], inspired by percolation and random walk theory, the asymptotic scaling form…”

Section: Why An Improved Method?mentioning

confidence: 99%

“…The empty graph is indeed the configuration from which we will start all simulations. For a simulation with the quartic action (17) we just have to replace (32) by…”

Section: Algorithm R For Real Nmentioning

confidence: 99%

Simulating the all-order strong coupling expansion IV: CP(N−1) as a loop model

Wolff

2010

Nuclear Physics B

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“…Worm algorithms were first applied to classical lattice models in [33], and it was demonstrated empirically in [34] that the worm algorithm is an extraordinarily efficient method for simulating the three-dimensional Ising model. See [35,36] for some recent applications to O(n) models. Worm algorithms provide a natural way to simulate cycle-space models.…”

Section: Introductionmentioning

confidence: 99%

Worm Monte Carlo study of the honeycomb-lattice loop model

2011

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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 n<2, on the critical line and in the densely-packed and fully-packed phases. By comparing our numerical results with Coulomb gas theory, we identify the exact scaling exponents governing some fundamental geometric and dynamic observables. In particular, we show that for all n<2, 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.Comment: 33 pages, 12 figure

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“…Numerical evidence presented in [54] also suggests it provides a very efficient method for studying the Ising two-point correlation function. Applications and extensions of the worm process now constitute an active topic in computational physics; see for example [19,50,4,2,51,52,53,55,56,20,27,12,28,49]. To our knowledge, however, no rigorous results have previously been reported on the mixing of the worm process.…”

Section: Introductionmentioning

confidence: 99%