Document Type

Article

Date of Original Version

3-1978

Abstract

In the early 1960’s one-dimensional model systems were regarded as amusing toys with the advantage of being far more easily solvable than their ’’real’’ three-dimensional counterparts. Now essentially 1-D (quasi-1-D) magnets can be ’’tailor-made’’ in the laboratory. Even more popular is the field of organic conductors like TTF⋅TCNQ, which are naturally quasi-1-D. Currently solitons and related solutions of non-linear, dispersive 1-D differential equations are ubiquitous in physics, including the area of 1-D magnetism. These developments are discussed in the Introduction. The rest of this paper is concerned with model Hamiltonians, model comparisons, critical singularities in 1-D (quasi-1-D) systems, accuracy of numerical techniques in comparison with exact solutions, brief accounts of dilute and disordered 1-D systems, and 1-D spin dynamics. Finally, a comment is made on a variety of interesting isomorphisms between 1-D magnets and phenomena in several other areas of physics, for example 2-D ferroelectrics, field-theoretic models, and realistic fluids. Comparison of theory and experiment has been the subject of several excellent reviews and is therefore not discussed here.

Publisher Statement

Copyright 1978 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.

The following article appeared in Journal of Applied Physics and may be found at http://dx.doi.org/10.1063/1.325026

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