2 5 Ja n 20 05 One - Dimensional Magnetism

We present an up-to-date survey of theoretical concepts and results in the field of one-dimensional magnetism and of their relevance to experiments and real materials. Main emphasis of the chapter is on quantum phenomena in models of localized spins with isotropic exchange and additional interactions from anisotropy and external magnetic fields. Three sections deal with the main classes of model systems for 1D quantum magnetism: S = 1/2 chains, spin chains with S > 1/2, and S = 1/2 Heisenberg ladders. We discuss the variation of physical properties and elementary excitation spectra with a large number of model parameters such as magnetic field, anisotropy, alternation, next-nearest neighbour exchange, etc. We describe the related quantum phase diagrams, which include some exotic phases of frustrated chains discovered during the last decade. A section on modified spin chains and ladders deals in particular with models including higher-order exchange interactions (ring exchange for S = 1/2 and biquadratic exchange for S = 1 systems), with spin-orbital models and mixed spin (ferrimagnetic) chains. The final section is devoted to gapped one-dimensional spin systems in high magnetic field. It describes such phenomena as magnetization plateaus and cusp singularities, the emergence of a critical phase when the excitation gap is closed by the applied field, and field-induced ordering due to weak three-dimensional coupling or anisotropy. We discuss peculiarities of the dynamical spin response in the critical and ordered phases.