  The Regge Calculus is a powerful method to approximate a continuous manifold
by a simplicial lattice, keeping the connectivities of the underlying lattice
fixed and taking the edge lengths as degrees of freedom. The Discrete Regge
Model limits the choice of the link lengths to a finite number. We examine the
phase structure of Standard Regge Calculus in four dimensions and compare our
Monte Carlo results with those of the $Z_2$-Regge Model as well as with another
formulation of lattice gravity derived from group theoretical considerations.
Within all of the three models of quantum gravity we find an extension of the
well-defined phase to negative gravitational couplings and a new phase
transition. We calculate two-point functions between geometrical quantities at
the corresponding critical point and estimate the masses of the respective
interaction particles. A main concern in lattice field theories is the
existence of a continuum limit which requires the existence of a continuous
phase transition. The recently conjectured second-order transition of the
four-dimensional Regge skeleton at negative gravity coupling could be such a
candidate. We examine this regime with Monte Carlo simulations and critically
discuss its behavior.
