PHASE-STRUCTURE OF DYNAMICAL TRIANGULATION MODELS IN 3 DIMENSIONS

The dynamical triangulation model of three-dimensional quantum gravity is shown to have a line of transitions in an expanded phase diagram w hich includes a coupling mu to the order of the vertices. Monte Carlo renormalization group and finite size scaling techniques are used to l ocate and characterize this line, Our results indicate that for mu < m u(1) similar to -1.0 the model is always in a crumpled phase independe nt of the value of the curvature coupling. For mu < 0 the results are in agreement with an approximate mean field treatment, We find evidenc e that this line corresponds to first-order transitions extending to p ositive mu. However, the behavior appears to change for mu > mu(2) sim ilar to 2.0-4,0, The simplest scenario that is consistent with the dat a is the existence of a critical end point. (C) 1998 Elsevier Science B.V.