Bosons in magnetism

Not long after S.N. Bose's work and the subsequent advent of quantum mechanics, it was realized that low-lying excitations in magnets are well described by Bose statistics. In this paper, we discuss this correspondence in the context of spin waves or magnons, which arise as Goldstone bosons as an outcome of a broken symmetry. Related implications for low-temperature thermodynamics in three dimensions, and for the loss of long range order in lower dimensions, are also discussed. In one dimension, we show that magnon bound states can be determined exactly using the Bethe ansatz. Further, a quantum phase transition induced in an antiferromagnet by the application of a uniform field is shown to be described by the Bose-Einstein condensation of triplon excitations. (author)