Magnetism in one dimension

Not just biological phenomena but most physical phenomena as well become drastically altered or impossible in spaces of fewer than three dimensions. As is well known, the cooperative behavior of many‐body systems depends very strongly on the coordination of the closely interacting particles and therefore on the number of spatial dimensions. As we shall see, not only does an examination of physics in fewer than three dimensions illuminate the familiar world of three dimensions, there are also real systems whose structure effectively reduces their dimensionality and for which, therefore, low‐dimensional physics is a prerequisite. As a consequence, a considerable effort has been expended in explaining the properties of lower‐dimensional and, especially, linear systems. During the last decade there has been a veritable explosion in the “one‐dimensional” literature. In this article we would like to discuss in the context of magnetism some of the motivating factors for this explosion and the progress that has been achieved so far.