Cluster algorithms for frustrated two dimensional Ising antiferromagnets via dual worm constructions

Abstract

We report on the development of two dual worm constructions that lead to cluster algorithms for efficient and ergodic Monte Carlo simulations of frustrated Ising models with arbitrary two-spin interactions that extend up to third-neighbours on the triangular lattice. One of these algorithms generalizes readily to other frustrated systems, such as Ising antiferromagnets on the Kagome lattice with further neighbour couplings. We characterize the performance of both these algorithms in a challenging regime with power-law correlations at finite wavevector.

arXiv comment16 2-column PRB format pages. 24 embedded figures

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Cited by in corpus (19)

• Solving frustrated Ising models using tensor networks
• Partial lifting of degeneracy in the $J_1-J_2-J_3$ Ising antiferromagnet on the kagome lattice
• Policy Guided Monte Carlo: Reinforcement Learning Markov Chain Dynamics
• Artificial out-of-plane Ising antiferromagnet on the kagome lattice with very small further neighbour couplings
• Spin-liquid behaviour and the interplay between Pokrovsky-Talapov and Ising criticality in the distorted, triangular-lattice, dipolar Ising antiferromagnet
• Bilayer Coulomb phase of two dimensional dimer models: Absence of power-law columnar order
• Unified tensor network theory for frustrated classical spin models in two dimensions
• Theory of charge-6e condensed phase in Kagome lattice superconductors
• Ashkin-Teller phase transition and multicritical behavior in a classical monomer-dimer model
• A quantum Monte Carlo algorithm for arbitrary spin-1/2 Hamiltonians
• Solution of Disordered Microphases in the Bethe approximation
• Geometric allocation approach to accelerating directed worm algorithm
• A universal black-box quantum Monte Carlo approach to quantum phase transitions
• Lifted directed-worm algorithm
• Flux roughening in spin ice with mixed $\pm J$ interactions
• Statistical properties of worm algorithms for two dimensional frustrated Ising models
• Emergent Intermediate Phase in the $J_1$-$J_2$ XY model from Tensor Network Approaches
• Flux fractionalization transition in anisotropic $S=1$ antiferromagnets and dimer-loop models
• Advanced measurement techniques in quantum Monte Carlo: The permutation matrix representation approach