Ising models coupled to two and three dimensional quantum gravity

Abstract

We present the results of numerical simulations aimed at understanding the nature of models encorporating Ising spins living on dynamical triangulations. In two dimensions we study multiple Ising systems in an effort to analyse the ‘c = 1’ barrier. We observe a significant coupling of the spins to the lattice which increases with the central charge. We also establish the phase diagram of three dimensional quantum gravity coupled to Ising matter. We find that in the negative curvature phase of quantum gravity the Ising spins order for arbitrary ferromagnetic coupling because the coordination number of the sites diverges. However in the postive curvature phase there is evidence for two spin phases separated by a first order transition.