4-DIMENSIONAL DYNAMICALLY TRIANGULATED GRAVITY COUPLED TO MATTER

We investigate the phase structure of four-dimensional quantum gravity coupled to Ising spins or Gaussian scalar fields by means of numerica l simulations. The quantum gravity part is modeled by the summation ov er random simplicial manifolds, and the matter fields are located in t he center of the four-simplices, which constitute the building blocks of the manifolds. We find that the coupling between spin and geometry is weak away from the critical point of the Ising model. At the critic al point there is clear coupling, which qualitatively agrees with that of Gaussian fields coupled to gravity. In the case of pure gravity a transition between a phase with highly connected geometry and a phase with very ''dilute'' geometry has been observed earlier. The nature of this transition seems unaltered when matter fields are included. It w as the hope that continuum physics could be extracted at the transitio n between the two types of geometries. The coupling to matter fields, at least in the form discussed in this paper, seems not to improve the scaling of the curvature at the transition point.