Fixed versus random triangulations in 2D Regge calculus

We study 2D quantum gravity on spherical topologies using the Regge calculus approach with the dll measure. Instead of a fixed non-regular triangulation which has been used before, we study for each system size four different random triangulations, which are obtained according to the standard Voronoi-Delaunay procedure. We compare both approaches quantitatively and show that the difference in the expectation value of R2 between the fixed and the random triangulation depends on the lattice size and the surface area A. We also try again to measure the string susceptibility exponents through a finite-size scaling Ansatz in the expectation value of an added R2 interaction term in an approach where A is held fixed. The string susceptibility exponent γ′str is shown to agree with theoretical predictions for the sphere, whereas the estimate for γstr appears to be too negative.