Phase structure of dynamical triangulation models in three dimensions

The dynamical triangulation model of three-dimensional quantum gravity is shown to have a line of transitions in an expanded phase diagram which includes a coupling μ to the order of the vertices. Monte Carlo renormalization group and finite size scaling techniques are used to locate and characterize this line. Our results indicate that for μ < μ₁ ∼ - 1.0 the model is always in a crumpled phase independent of the value of the curvature coupling. For μ < 0 the results are in agreement with an approximate mean field treatment. We find evidence that this line corresponds to first-order transitions extending to positive μ. However, the behavior appears to change for μ > μ₂ ∼ 2.0-4.0. The simplest scenario that is consistent with the data is the existence of a critical end point.