Advances In Physics · 1974 · 2.2K citations · 346 references
Natural SciencesPhysicsCondensed Matter PhysicsMagnetic MaterialsTheoretical PhysicsAntiferromagnetic MaterialsAntiferromagnetismExchange InteractionsFerromagnetismMagnetic Properties Of SolidsMagnetism In SolidsExchange Interactions In Heisenberg ModelsHeisenberg AntiferromagnetHeisenberg MagnetismHeisenberg ModelIsing MagnetismIsing ModelLow-dimensional MagnetismTwo-dimensional Magnetism
Abstract “…. For the truth of the conclusions of physical science, observation is the supreme Court of Appeal….” (Sir Arthur Eddington, The Philosophy of Physical Science.) In this paper we shall review the theoretical and experimental results obtained on simple magnetic model systems. We shall consider the Heisenberg, XY and Ising type of interaction (ferro and antiferromagnetic), on magnetic lattices of dimensionality 1, 2 and 3. Particular attention will be paid to the approximation of these model systems in real crystals, viz. how they can be realized or be expected to exist in nature. A large number of magnetic compounds which, according to the available experimental information, meet the requirements set by one or the other of the various models are considered and their properties discussed. Many examples will be given that demonstrate to what extent experiments on simple magnetic systems support theoretical descriptions of magnetic ordering phenomena and contribute to their understanding. It will also be indicated in which direction there is a need and/or a possibility for future work.
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Linear Magnetic Chains with Anisotropic Coupling
Jill C. Bonner, Michael E. Fisher · Physical Review · 1964 · 2.5K citations · Full text
Existence of Long-Range Order in One and Two Dimensions
P. C. Hohenberg · Physical Review · 1967 · 2.4K citations