3-Dimensional Quantum-Gravity Coupled To Ising Matter

We establish the phase diagram of three-dimensional quantum gravity coupled to Ising matter. We find that in the negative curvature phase of the quantum gravity there is no disordered phase for ferromagnetic Ising matter because the coordination number of the sites diverges. In the positive curvature phase of the quantum gravity there is evidence for two spin phases with a first-order transition between them