Measuring the string susceptibility in 2D simplicial quantum gravity using the Regge approach Original Research Article

We use Monte Carlo simulations to study pure 2D Euclidean quantum gravity with R2-interaction on spherical topologies, employing Reggeʹs formulation. We attempt to measure the string susceptibility exponent γstr by using a finite-size scaling Ansatz in the expectation value of R2, as has been done in a previous study by Bock and Vink (Nucl. Phys. B 438 (1995) 320). By considerably extending the range and statistics of their study we find that this Ansatz is plagued by large systematic errors. The R2 specific string susceptibility exponent γstr′ is found to agree with theoretical predictions, but its determination also is subject to large systematic errors and the presence of finite-size scaling corrections. To circumvent this obstacle we suggest a new scaling Ansatz which in principle should be able to predict both, γstr and γstr′. First results indicate that this requires large system sizes to reduce the uncertainties in the finite-size scaling Ansätze. Nevertheless, our investigation shows that within the achievable accuracy the numerical estimates are still compatible with analytic predictions, contrary to the recent claim by Bock and Vink.