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- Geometrical_frustration abstract "In condensed matter physics, the term geometrical frustration (or in short: frustration) refers to a phenomenon, where atoms tend to stick to non-trivial positions or where, on a regular crystal lattice, conflicting inter-atomic forces (each one favoring rather simple, but different structures) lead to quite complex structures. As a consequence of the frustration in the geometry or in the forces, a plenitude of distinct ground states may result at zero temperature, and usual thermal ordering may be suppressed at higher temperatures. Much studied examples are amorphous materials, glasses, or dilute magnets.The term frustration, in the context of magnetic systems, has been introduced by Gerard Toulouse (1977). Indeed, frustrated magnetic systems had been studied even before. Early work includes a study of the Ising model on a triangular lattice with nearest-neighbor spins coupled antiferromagnetically, by G. H. Wannier, published in 1950. Related features occur in magnets with competing interactions, where both ferro- as well as antiferromagnetic couplings between pairs of spins or magnetic moments are present, with the type of interaction depending on the separation distance of the spins. In that case commensurability, such as helical spin arrangements may result, as had been discussed originally, especially, by A. Yoshimori, T. A. Kaplan, R. J. Elliott, and others, starting in 1959, to describe experimental findings on rare-earth metals. A renewed interest in such spin systems with frustrated or competing interactions arose about two decades later, beginning in the 70s of the 20th century, in the context of spin glasses and spatially modulated magnetic superstructures. In spin glasses, frustration is augmented by stochastic disorder in the interactions, as may occur, experimentally, in non-stoichiometric magnetic alloys. Carefully analyzed spin models with frustration include the Sherrington-Kirkpatrick model, describing spin glasses, and the ANNNI model, describing commensurability magnetic superstructures.".
- Geometrical_frustration thumbnail Triangular_frustration.svg?width=300.
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- Geometrical_frustration wikiPageOutDegree "82".
- Geometrical_frustration wikiPageRevisionID "688305096".
- Geometrical_frustration wikiPageWikiLink 600-cell.
- Geometrical_frustration wikiPageWikiLink ANNNI_model.
- Geometrical_frustration wikiPageWikiLink Alloy.
- Geometrical_frustration wikiPageWikiLink Amorphous_solid.
- Geometrical_frustration wikiPageWikiLink Antiferromagnetism.
- Geometrical_frustration wikiPageWikiLink Atom.
- Geometrical_frustration wikiPageWikiLink Calorimeter.
- Geometrical_frustration wikiPageWikiLink Category:Condensed_matter_physics.
- Geometrical_frustration wikiPageWikiLink Category:Thermodynamic_entropy.
- Geometrical_frustration wikiPageWikiLink Close-packing_of_equal_spheres.
- Geometrical_frustration wikiPageWikiLink Commensurability_(mathematics).
- Geometrical_frustration wikiPageWikiLink Condensed_matter_physics.
- Geometrical_frustration wikiPageWikiLink Crystal_field_theory.
- Geometrical_frustration wikiPageWikiLink Crystal_structure.
- Geometrical_frustration wikiPageWikiLink Cubic_crystal_system.
- Geometrical_frustration wikiPageWikiLink Degenerate_energy_levels.
- Geometrical_frustration wikiPageWikiLink Dysprosium_titanate.
- Geometrical_frustration wikiPageWikiLink Entropy.
- Geometrical_frustration wikiPageWikiLink Ferromagnetism.
- Geometrical_frustration wikiPageWikiLink Gauge_theory.
- Geometrical_frustration wikiPageWikiLink Geometrical_frustration.
- Geometrical_frustration wikiPageWikiLink Gerard_Toulouse.
- Geometrical_frustration wikiPageWikiLink Glass.
- Geometrical_frustration wikiPageWikiLink Golden_ratio.
- Geometrical_frustration wikiPageWikiLink Gregory_Wannier.
- Geometrical_frustration wikiPageWikiLink Ground_state.
- Geometrical_frustration wikiPageWikiLink Harold_Scott_MacDonald_Coxeter.
- Geometrical_frustration wikiPageWikiLink Heat_capacity.
- Geometrical_frustration wikiPageWikiLink Helimagnetism.
- Geometrical_frustration wikiPageWikiLink Hexagon.
- Geometrical_frustration wikiPageWikiLink Hexagonal_crystal_system.
- Geometrical_frustration wikiPageWikiLink Holmium_stannate.
- Geometrical_frustration wikiPageWikiLink Holmium_titanate.
- Geometrical_frustration wikiPageWikiLink Ice.
- Geometrical_frustration wikiPageWikiLink Ice_rules.
- Geometrical_frustration wikiPageWikiLink Ising_model.
- Geometrical_frustration wikiPageWikiLink Latent_heat.
- Geometrical_frustration wikiPageWikiLink Line_(geometry).
- Geometrical_frustration wikiPageWikiLink Linus_Pauling.
- Geometrical_frustration wikiPageWikiLink Magnet.
- Geometrical_frustration wikiPageWikiLink Magnetic_force_microscope.
- Geometrical_frustration wikiPageWikiLink Magnetic_moment.
- Geometrical_frustration wikiPageWikiLink Magnetism.
- Geometrical_frustration wikiPageWikiLink Miller_index.
- Geometrical_frustration wikiPageWikiLink Order_and_disorder_(physics).
- Geometrical_frustration wikiPageWikiLink Oxygen.
- Geometrical_frustration wikiPageWikiLink Pentagon.
- Geometrical_frustration wikiPageWikiLink Picometre.
- Geometrical_frustration wikiPageWikiLink Polytope.
- Geometrical_frustration wikiPageWikiLink Pyrochlore.
- Geometrical_frustration wikiPageWikiLink Quantum_chromodynamics.
- Geometrical_frustration wikiPageWikiLink Quasicrystal.
- Geometrical_frustration wikiPageWikiLink RKKY_interaction.
- Geometrical_frustration wikiPageWikiLink Roger_James_Elliott.
- Geometrical_frustration wikiPageWikiLink Schläfli_symbol.
- Geometrical_frustration wikiPageWikiLink Signed_graph.
- Geometrical_frustration wikiPageWikiLink Spin_(physics).
- Geometrical_frustration wikiPageWikiLink Spin_glass.
- Geometrical_frustration wikiPageWikiLink Spin_ice.
- Geometrical_frustration wikiPageWikiLink Stochastic.
- Geometrical_frustration wikiPageWikiLink Stoichiometry.
- Geometrical_frustration wikiPageWikiLink Tetrahedron.
- Geometrical_frustration wikiPageWikiLink Triangular_tiling.
- Geometrical_frustration wikiPageWikiLink Trihexagonal_tiling.
- Geometrical_frustration wikiPageWikiLink Wilson_loop.
- Geometrical_frustration wikiPageWikiLink Ångström.
- Geometrical_frustration wikiPageWikiLink File:FrustrationIcosaedre.jpg.
- Geometrical_frustration wikiPageWikiLink File:FrustrationPentagons.jpg.
- Geometrical_frustration wikiPageWikiLink File:Schlegel_wireframe_600-cell_vertex-centered.png.
- Geometrical_frustration wikiPageWikiLink File:SpinIce.svg.
- Geometrical_frustration wikiPageWikiLink File:Water_ice.png.
- Geometrical_frustration wikiPageWikiLinkText "Geometrical frustration".
- Geometrical_frustration wikiPageWikiLinkText "Geometrically frustrated".
- Geometrical_frustration wikiPageWikiLinkText "frustrate".
- Geometrical_frustration wikiPageWikiLinkText "frustrated interactions".
- Geometrical_frustration wikiPageWikiLinkText "frustrated magnetism".
- Geometrical_frustration wikiPageWikiLinkText "frustrated magnets".
- Geometrical_frustration wikiPageWikiLinkText "frustrated".
- Geometrical_frustration wikiPageWikiLinkText "frustration".
- Geometrical_frustration wikiPageWikiLinkText "geometrical frustration".
- Geometrical_frustration wikiPageWikiLinkText "geometrically frustrated magnets".
- Geometrical_frustration wikiPageWikiLinkText "geometrically frustrated".
- Geometrical_frustration align "right".
- Geometrical_frustration caption "Figure 1: Antiferromagnetically interacting spins in a triangular arrangement".
- Geometrical_frustration caption "Figure 2: Antiferromagnetically interacting spins in a tetrahedral arrangement".
- Geometrical_frustration caption "Figure 3: Spins along the easy axes of a tetrahedron".
- Geometrical_frustration caption "Figure 4: Frustrated easy spins in a tetrahedron".
- Geometrical_frustration direction "horizontal".
- Geometrical_frustration image "Spinice.png".
- Geometrical_frustration image "Triangular frustration.svg".
- Geometrical_frustration image "allinspintet.svg".
- Geometrical_frustration image "frustratedtetrahedron.png".
- Geometrical_frustration width "150".
- Geometrical_frustration wikiPageUsesTemplate Template:Multiple_image.