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

TL;DR

This paper uses Monte Carlo simulations with Regge calculus to measure the string susceptibility exponent in 2D quantum gravity, finding results compatible with theoretical predictions but highlighting challenges due to systematic errors and finite-size effects.

Contribution

The study introduces a new scaling Ansatz to better estimate string susceptibility exponents in 2D quantum gravity using Regge calculus, improving upon previous methods.

Findings

The traditional finite-size scaling Ansatz is affected by large systematic errors.

The new scaling Ansatz shows promise but requires larger system sizes for accurate predictions.

Numerical results are consistent with analytic predictions within current uncertainties.

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 $\gamma_{\rm str}$ 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 Ans\"atze. 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.