A survey of analytic results for the 1-D Heisenberg magnets (invited)

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Abstract
The linear, nearest‐neighbor, magnetic systems described by the anisotropic, finite‐field, spin‐1/2, Heisenberg Hamiltonian H = Σi(SxiSxi+1+SyiSyi+1+ΔSziSzi+1 ) −HoΣiSzi, −∞<Δ<∞ and 0?H0, are increasingly attracting attention, both experimentally and theoretically. These systems are now known to be intimately related to models in quantum field theory, for quantum solitons, and for other many‐body problems. In its own right, the Hamiltonian describes many physically realized systems; thus the theoretical prediction of some unexpected and interesting properties indicates experimental possibilities. We outline what has been learned, from the method of Bethe’s Ansatz, of the ground state, elementary excitations, and low‐temperature thermodynamics as functions of Δ and Ho. We discuss the changes in behavior of the low‐temperature thermodynamics as Δ and Ho are varied and give the relationship of these changes to the ground state and excitation spectrum characteristics. In small magnetic fields, unexpected structure in the low‐temperature thermodynamics of the ferromagnetic Heisenberg magnet has been predicted.