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

Abstract

We use Monte Carlo simulations to study pure 2D Euclidean quantum gravity with $R^2$-interaction on spherical topologies, employing Regge's formulation. We attempt to measure the string susceptibility exponent ${\gamma }_{\mathrm{str}}$ by using a finite-size scaling Ansatz in the expectation value of $R^2$, as has been done in a previous study by Bock and Vink ( hep-lat/9406018 ). By considerably extending the range and statistics of their study we find that this Ansatz is plagued by large systematic errors. The $R^2$ specific string susceptibility exponent $\GS'$ 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, $\GS$ and $\GS'$. 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.

33 pages, self unpacking uuencoded PostScript file, including all the figures. Paper also available at http://www.physik.fu-berlin.de/~holm/

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Cited by in corpus (8)

• On the Measure in Simplicial Gravity
• On the Gravitational Scaling Dimensions
• Spikes in Quantum Regge Calculus
• Fixed versus random triangulations in 2D simplicial Regge calculus
• Multicanonical simulation of 3D dynamical triangulation model and a new phase structure
• Z_2-Regge versus Standard Regge Calculus in two dimensions
• 2D Lorentzian Gravity as 2D Euclidean Gravity with Ising Spins
• Simplicial Quantum Gravity on a Randomly Triangulated Sphere