Monte Carlo Simulations of 2-Dimensional Quantum Gravity Coupled to $c = 1$ Matter

TL;DR

This paper reports high-precision Monte Carlo simulations of 2D quantum gravity coupled to a scalar field, analyzing geometric and correlation properties to test theoretical predictions.

Contribution

It provides detailed numerical results for 2D quantum gravity with $c=1$ matter, comparing simulations with conformal field theory and matrix model predictions.

Findings

Mean square extent matches theoretical expectations.

Correlation functions agree with conformal field theory.

Results support universality of the model's leading behavior.

Abstract

We present results of a high precision Monte Carlo simulation of dynamically triangulated random surfaces (up to $\approx$ 34,000 triangles) coupled to one scalar field ($c=1$). The mean square extent has been measured for different actions to test the universality of the leading term as a function of the size of the surfaces. Furthermore, the integrated 2-point correlation function for vertex operators is compared with conformal field theory and matrix model predictions.