Exact Solution of the Infinite-Range Quantum Mattis Model

We have solved the quantum version of the Mattis model with infinite-range interactions. A variational approach gives the exact solution for the infinite-range system, in spite of the non-commutative nature of the quantum spin components; this implies that quantum effects are not predominant in determining the macroscopic properties of the system. Nevertheless, the model has a surprisingly rich phase behaviour, exhibiting phase diagrams with tricritical, three-phase and critical end points.