Regge gravity on general triangulations

We investigate quantum gravity in four dimensions using the Regge approach on triangulations of the four-torus with general, non-regular incidence matrices. We observe that the simplicial lattice with originally 31 regular vertices tends to develop spikes at irregularly inserted vertices with low coordination numbers even for vanishing gravitational coupling. Different to the regular, hypercubic lattices almost exclusively used in previous studies, we find now that the observables depend on the measure. Computations with nonvanishing gravitational coupling still reveal the existence of a region with well-defined expectation values. However, the phase structure depends on the triangulation with the regular and additional vertices undergoing two separate transitions. Even with additional higher-order terms in the action the critical behavior of the system changes with varying (local) coordination numbers.