A worm algorithm for the fully-packed loop model

Abstract

We present a Markov-chain Monte Carlo algorithm of worm type that correctly simulates the fully-packed loop model on the honeycomb lattice, and we prove that it is ergodic and has uniform stationary distribution. The fully-packed loop model on the honeycomb lattice is equivalent to the zero-temperature triangular-lattice antiferromagnetic Ising model, which is fully frustrated and notoriously difficult to simulate. We test this worm algorithm numerically and estimate the dynamic exponent z = 0.515(8). We also measure several static quantities of interest, including loop-length and face-size moments. It appears numerically that the face-size moments are governed by the magnetic dimension for percolation.

31 pages, 10 figures. Several new figures added, and some minor typos corrected. Uses the following latex packages: algorithm.sty, algorithmic.sty, elsart-num.bst, elsart1p.cls, elsart.cls

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Cited by in corpus (8)

• Topological aspects of symmetry breaking in triangular-lattice Ising antiferromagnets
• Disorder driven spin-orbital liquid behaviour in the Ba${}_3$XSb${}_2$O${}_9$ materials
• Worm Monte Carlo study of the honeycomb-lattice loop model
• Spin-liquid behaviour and the interplay between Pokrovsky-Talapov and Ising criticality in the distorted, triangular-lattice, dipolar Ising antiferromagnet
• Classical-quantum correspondence of special and extraordinary-log criticality: Villain's bridge
• Worm-type Monte Carlo simulation of the Ashkin-Teller model on the triangular lattice
• Flux roughening in spin ice with mixed $\pm J$ interactions
• Solvable models for 2+1D quantum critical points: Loop soups of 1+1D conformal field theories