Phase Structure of Four Dimensional Simplicial Quantum Gravity

TL;DR

This paper investigates the phase structure of four-dimensional Euclidean quantum gravity using Monte Carlo simulations of triangulations, revealing two distinct phases with different geometric scaling behaviors and identifying a finite size scaling exponent.

Contribution

The study provides new high-statistics Monte Carlo evidence for phase transitions and scaling behaviors in four-dimensional simplicial quantum gravity models.

Findings

Identification of two distinct phases with different scaling laws

Evidence of a phase transition characterized by a susceptibility peak

Extraction of a finite size scaling exponent

Abstract

We present the results of a high statistics Monte Carlo study of a model for four dimensional euclidean quantum gravity based on summing over triangulations. We show evidence for two phases; in one there is a logarithmic scaling on the mean linear extent with volume, whilst the other exhibits power law behaviour with exponent 1/2. We are able to extract a finite size scaling exponent governing the growth of the susceptibility peak