Anisotropic Heisenberg Magnet with Long-Range Interactions. Integrability and Phase Structure

We show that the xxz Heisenberg magnet withlong-range interactions in a magnetic field, isintegrable both classically and quantum mechanically.Explicit expressions are given for the involutiveintegrals of the motion. The nature of the spectrum andthe ground state are clarified and the partitionfunction is calculated exactly in the thermodynamiclimit. A detailed study of the phase structure of thesystem is also performed.