Cluster simulations of loop models on two-dimensional lattices

Abstract

We develop cluster algorithms for a broad class of loop models on two-dimensional lattices, including several standard O(n) loop models at n \ge 1. We show that our algorithm has little or no critical slowing-down when 1 \le n \le 2. We use this algorithm to investigate the honeycomb-lattice O(n) loop model, for which we determine several new critical exponents, and a square-lattice O(n) loop model, for which we obtain new information on the phase diagram.

LaTex2e, 4 pages; includes 1 table and 2 figures. Totally rewritten in version 2, with new theory and new data. Version 3 as published in PRL

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Cited by in corpus (27)

• Machine learning of phase transitions in the percolation and XY models
• Unsupervised learning of topological phase transitions using Calinski-Harabaz index
• Worm Monte Carlo study of the honeycomb-lattice loop model
• The O(n) loop model on a three-dimensional lattice
• Dynamic critical behavior of the Chayes-Machta-Swendsen-Wang algorithm
• Tethered Monte Carlo: computing the effective potential without critical slowing down
• Phase transition in site-diluted Josephson junction arrays: A numerical study
• Loop-Cluster Coupling and Algorithm for Classical Statistical Models
• The Hintermann-Merlini-Baxter-Wu and the Infinite-Coupling-Limit Ashkin-Teller Models
• A worm algorithm for the fully-packed loop model
• Stability and Loop Models from Decohering Non-Abelian Topological Order
• Backbone and shortest-path exponents of the two-dimensional $Q$-state Potts model
• Percolation and critical O($n$) loop configurations
• Potts and percolation models on bowtie lattices
• Worm-type Monte Carlo simulation of the Ashkin-Teller model on the triangular lattice
• Bridges in the random-cluster model
• Tricritical O(n) models in two dimensions
• Percolation of the Site Random-Cluster Model by Monte Carlo Method
• Universal critical properties of the Eulerian bond-cubic model
• Correction-to-scaling exponent for percolation and the Fortuin--Kasteleyn Potts model in two dimensions
• Exact critical points of the O($n$) loop model on the martini and the 3-12 lattices
• A cluster Monte Carlo algorithm with a conserved order parameter
• Ising-like phase transition of an n-component Eulerian face-cubic model
• Critical Line of the O($N$) Loop Model on the Square Lattice
• Geometric Exponents of Dilute Logarithmic Minimal Models
• Computational Study of a Multistep Height Model
• Phase transitions in 3D Ising model with cluster weight by Monte Carlo method