On the Phase Diagram of Three-Dimensional Simplicial Quantum Gravity

The phase diagram of three-dimensional (3d) simplicial quantum gravity is studied using the Monte–Carlo simulation method. It is found that the behavior of the entropy of manifolds, unambiguously defined in this discrete formulation, insures the existence of a vacuum, in spite of the Einstein action being bottomless. A critical line is found as well as some evidence for the existence of a tricritical point. Only to the right of this point, where the bare coupling of the Einstein term in the action is strong enough, a sensible continuum limit can possibly exist.