Classical Topological Order in Kagome Ice

Abstract

We examine the onset of classical topological order in a nearest-neighbor kagome ice model. Using Monte Carlo simulations, we characterize the topological sectors of the groundstate using a non-local cut measure which circumscribes the toroidal geometry of the simulation cell. We demonstrate that simulations which employ global loop updates that are allowed to wind around the periodic boundaries cause the topological sector to fluctuate, while restricted local loop updates freeze the simulation into one topological sector. The freezing into one topological sector can also be observed in the susceptibility of the real magnetic spin vectors projected onto the kagome plane. The ability of the susceptibility to distinguish between fluctuating and non-fluctuating topological sectors should motivate its use as a local probe of topological order in a variety of related model and experimental systems.

17 pages, 9 figures

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• Kagome qubit ice
• Dynamic scaling of topological ordering in classical systems
• Curie-law crossover in spin liquids
• Policy Guided Monte Carlo: Reinforcement Learning Markov Chain Dynamics
• Reentrance of disorder in the anisotropic shuriken Ising model
• Engineering topological phase transition and Aharonov-Bohm caging in a flux-staggered lattice
• A Large-$S$ Study of Quantum Kagome Ice
• A generalized Monte Carlo loop algorithm for frustrated Ising models
• Theory of quantum kagome ice and vison zero modes
• The Concept of Spin Ice Graphs and a Field Theory for their Topological Monopoles and Charges
• Tunable critical correlations in kagome ice
• Universal Renyi mutual information in classical systems: the case of kagome ice
• Experimental Measures of Topological Sector Fluctuations in the F-Model
• Emergent Snake Magnetic Domains in Canted Kagome Ice