Monte Carlo simulation of ice models

Abstract

We propose a number of Monte Carlo algorithms for the simulation of ice models and compare their efficiency. One of them, a cluster algorithm for the equivalent three colour model, appears to have a dynamic exponent close to zero, making it particularly useful for simulations of critical ice models. We have performed extensive simulations using our algorithms to determine a number of critical exponents for the square ice and F models.

32 pages including 15 postscript figures, typeset in LaTeX2e using the Elsevier macro package elsart.cls

References in corpus (1)

• Liouville Field Theory of Fluctuating Loops

Cited by in corpus (76)

• Magnetic Pyrochlore Oxides
• Pyrochlore Photons: The U(1) Spin Liquid in a S=1/2 Three-Dimensional Frustrated Magnet
• Ising models of quantum frustration
• Spin Correlations in Ho${}_2$Ti${}_2$O${}_7$: a Dipolar Spin Ice System
• Long Range Order at Low Temperature in Dipolar Spin Ice
• Magnetic multipole analysis of kagome and artificial ice dipolar arrays
• Thermodynamic Properties of the Dipolar Spin Ice Model
• Machine Learning for Quantum Matter
• A Three Dimensional Kasteleyn Transition: Spin Ice in a [100] Field
• Vertex dynamics in finite two dimensional square spin ices
• Directed-loop Monte Carlo simulations of vertex models
• Analysis of a fully packed loop model arising in a magnetic Coulomb phase
• FePd${}_3$ as a material for thermally active artificial spin ice
• Magnetic charge and ordering in kagome spin ice
• Pocket Monte Carlo algorithm for classical doped dimer models
• Quantum strings in quantum spin ice
• Thermodynamics of elementary excitations in artificial magnetic square ice
• Extended quantum U(1)-liquid phase in a three-dimensional quantum dimer model
• From confinement to deconfinement of magnetic monopoles in artificial rectangular spin ices
• New physics in frustrated magnets: Spin ices, monopoles, etc
• Extending spin ice concepts to another geometry: the artificial triangular spin ice
• When opposites repel: from metastability to extended chiral spin textures in spin ice with short-range topological-defect interactions
• Quantum Anomalous Hall Effect in Kagome Ice
• Clustering of Topological Charges in a Kagome Classical Spin Liquid
• Order-by-disorder and quantum Coulomb phase in quantum square ice
• AC Wien effect in spin ice, manifest in non-linear non-equilibrium susceptibility
• Effect of long-and short-range interactions on the thermodynamics of dipolar spin ice
• Curie-law crossover in spin liquids
• Policy Guided Monte Carlo: Reinforcement Learning Markov Chain Dynamics
• Spinon walk in quantum spin ice
• Orbital ice: an exact Coulomb phase on the diamond lattice
• A Worm Algorithm for Two-Dimensional Spin Glasses
• The density profile of the six vertex model with domain wall boundary conditions
• Generation of ice states through deep reinforcement learning
• Frustrated colloidal ordering and fully packed loops in arrays of optical traps
• Confinement of monopoles and scaling theory near unconventional critical points
• Phase separation in the six-vertex model with a variety of boundary conditions
• Topologically stable ergodicity breaking from emergent higher-form symmetries in generalized quantum loop models
• Static properties of 2D spin-ice as a sixteen-vertex model
• Kosterlitz-Thouless transition of magnetic dipoles on the two-dimensional plane
• The 3D Kasteleyn transition in dipolar spin ice: a numerical study with the Conserved Monopoles Algorithm
• Ferromagnetic Coulomb phase in classical spin ice
• Simulating the Transverse Field Ising Model on the Kagome Lattice using a Programmable Quantum Annealer
• Classical topological order of the Rys F-model and its breakdown in realistic spin ice: Topological sectors of Faraday loops
• A numerical study of the F-model with domain-wall boundaries
• The square-lattice F model revisited: a loop-cluster update scaling study
• Seeing beyond the light: Vison and photon electrodynamics in quantum spin ice
• Itinerant electrons in the Coulomb phase
• Monte Carlo study of degenerate groundstates and residual entropy in a frustrated honeycomb lattice Ising model
• Monte Carlo study of the discontinuous quantum phase transition in the transverse-field Ising model on the pyrochlore lattice
• Loop algorithm for classical Heisenberg models with spin-ice type degeneracy
• Enhancing the formation of ionic defects to study the ice Ih/XI transition with molecular dynamics simulations
• Half-Magnetization Plateau of a Dipolar Spin Ice in a [100] Field
• Metal-insulator transition caused by the coupling to localized charge-frustrated systems under ice-rule local constraint
• Exotic magnetic phases in an Ising-spin Kondo lattice model on a kagome lattice
• Universal monopole scaling near transitions from the Coulomb phase
• A cluster algorithm for Monte Carlo simulations of spin ice
• Polarization Plateaus in Hexagonal Water Ice $I_h$
• Tuning the two-step melting of magnetic orders in a dipolar kagome spin ice by quantum fluctuations
• A generalized Monte Carlo loop algorithm for frustrated Ising models
• Investigation of the monopole magneto-chemical potential in spin ices using capacitive torque magnetometry
• Thermodynamics and fractal dynamics of nematic spin ice, a doubly frustrated pyrochlore Ising magnet
• On the Degeneracy of Spin Ice Graphs, and its Estimate via the Bethe Permanent
• Thermodynamics of two lattice ice models in three dimensions
• Loop algorithm for classical antiferromagnetic Heisenberg models with biquadratic interactions
• Vertex Models and Random Labyrinths: Phase Diagrams for Ice-type Vertex Models
• Classical fully-packed loop model with attractive interactions on the square lattice
• Energetic analysis of disorder effects in an artificial spin ice with dipolar interactions
• Statistical properties of worm algorithms for two dimensional frustrated Ising models
• A short-loop algorithm for quantum Monte Carlo simulations
• Flux roughening in spin ice with mixed $\pm J$ interactions
• Vortex Dynamics and Entropic Coulomb Forces in Ising and Potts Antiferromagnets and Ice Models
• On the Stability of Quantum Hall Kagome-ice Insulator
• Anisotropic Spin Ice on a Breathing Pyrochlore Lattice
• Thermodynamic Properties of Ice: A Monte Carlo Study
• Torpid Mixing of Markov Chains for the Six-vertex Model on ${\mathbb{Z}}^2$