REGGE GRAVITY ON GENERAL TRIANGULATIONS

We investigate quantum gravity in four dimensions using the Regge appr oach on triangulations of the four-torus with general, non-regular inc idence matrices. We observe that the simplicial lattice with originall y 31 regular vertices tends to develop spikes at irregularly inserted vertices with low coordination numbers even for vanishing gravitationa l coupling. Different to the regular, hypercubic lattices almost exclu sively used in previous studies, we find now that the observables depe nd on the measure. Computations with nonvanishing gravitational coupli ng still reveal the existence of a region with well-defined expectatio n values. However, the phase structure depends on the triangulation wi th the regular and additional vertices undergoing two separate transit ions. Even with additional higher-order terms in the action the critic al behavior of the system changes with varying (local) coordination nu mbers.