Phases of four-dimensional simplicial quantum gravity

The phase diagram and critical exponents for pure simplicial quantum gravity (Regge calculus) in four dimensions are discussed. In the small-$G$ phase, where $G$ is the bare Newton's constant, the simplices are collapsed and no continuum limit exists. In the large-$G$ phase the ground state appears to be well behaved, and the curvature goes to zero continuously as the critical value of $G$ is approached. Fluctuations in the curvature diverge at the critical point, while volume fluctuations remain finite. The critical exponents at the transition are estimated, and appear to be independent of the strength of the higher-derivative coupling $a$. With the lattice analogue of the DeWitt gravitational measure and for large enough $G$, the lattice higher-derivative theories ($a>\mathrm{}0\mathrm{}$) and the reflection-positive pure Regge theory ($a=0\mathrm{}$) appear to belong to the same phase for large enough $G$, which would suggest a common, unitary quantum continuum limit.