Anisotropic Heisenberg magnet with long-range interactions. Integrability and phase structure

We show that the xxz Heisenberg magnet with long-range interactions in a ma gnetic field, is integrable both classically and quantum mechanically. Expl icit expressions are given for the involutive integrals of the motion. The nature of the spectrum and the ground state are clarified and the partition function is calculated exactly in the thermodynamic limit. A detailed stud y of the phase structure of the system is also performed.