Classical-Quantum Mappings for Geometrically Frustrated Systems: Spin Ice in a [100] Field

Abstract

Certain classical statistical systems with strong local constraints are known to exhibit Coulomb phases, where long-range correlation functions have power-law forms. Continuous transitions from these into ordered phases cannot be described by a naive application of the Landau-Ginzburg-Wilson theory, since neither phase is thermally disordered. We present an alternative approach to a critical theory for such systems, based on a mapping to a quantum problem in one fewer spatial dimensions. We apply this method to spin ice, a magnetic material with geometrical frustration, which exhibits a Coulomb phase and a continuous transition to an ordered state in the presence of a magnetic field applied in the [100] direction.

15 pages, 4 figures; to be published in Phys. Rev. B; v2: added comments about thermal fluctuations out of spin ice states

References in corpus (9)

• Spin Ice State in Frustrated Magnetic Pyrochlore Materials
• Magnetic Monopoles in Spin Ice
• Dipolar spin correlations in classical pyrochlore magnets
• Coulomb and Liquid Dimer Models in Three Dimensions
• Power-law spin correlations in pyrochlore antiferromagnets
• Why spin ice obeys the ice rules
• Weakly Interacting, Dilute Bose Gases in 2D
• A Three Dimensional Kasteleyn Transition: Spin Ice in a [100] Field
• Unconventional continuous phase transition in a three dimensional dimer model

Cited by in corpus (27)

• The "Coulomb phase" in frustrated systems
• Coulomb gas transitions in three-dimensional classical dimer models
• Gauge theory picture of an ordering transition in a dimer model
• Topological Sector Fluctuations and Curie Law Crossover in Spin Ice
• Spin ice under pressure: symmetry enhancement and infinite order multicriticality
• Unconventional Quantum Critical Points
• Fragmentation in Frustrated Magnets -- A review
• Topological aspects of symmetry breaking in triangular-lattice Ising antiferromagnets
• SU(2)-invariant continuum theory for an unconventional phase transition in a three-dimensional classical dimer model
• Higgs transitions of spin ice
• Spin Ice Thin Film: Surface Ordering, Partial Magnetic Wetting and Emergent Square Ice
• Classical to quantum mapping for an unconventional phase transition in a three-dimensional classical dimer model
• Ultrasonic investigations of spin-ices Dy${}_2$Ti${}_2$O${}_7$ and Ho${}_2$Ti${}_2$O${}_7$ in and out of equilibrium
• Spin-liquid behaviour and the interplay between Pokrovsky-Talapov and Ising criticality in the distorted, triangular-lattice, dipolar Ising antiferromagnet
• Confinement of monopoles and scaling theory near unconventional critical points
• Ferromagnetic Coulomb phase in classical spin ice
• Emergence of cooperative dynamics in fully packed classical dimers
• Half-Magnetization Plateau of a Dipolar Spin Ice in a [100] Field
• Universal monopole scaling near transitions from the Coulomb phase
• Spin ice in a general applied magnetic field: Kasteleyn transition, magnetic torque and rotational magnetocaloric effect
• Tunable critical correlations in kagome ice
• Perfectly hidden order and Z2 confinement transition in a fully packed monopole liquid
• Quantum Kasteleyn transition
• Crossover from string to cluster dynamics following a field quench in spin ice
• Mean-field theory for confinement transitions and magnetization plateaux in spin ice
• Dynamic scaling theory for a field quench near the Kasteleyn transition in spin ice
• Dynamic scaling near the Kasteleyn transition in spin ice: critical relaxation of monopoles and strings following a field quench