Non-uniform measure in 4d simplicial quantum gravity

TL;DR

This paper explores how introducing a non-uniform measure in 4D simplicial quantum gravity affects phase transitions and critical behavior in a Monte Carlo simulation.

Contribution

It implements a non-uniform measure in 4D simplicial quantum gravity and analyzes its impact on phase transition properties.

Findings

Shifted transition region from hot to cold phase

Altered criticality of the phase transition

Demonstrated effects on geometric aspects

Abstract

Four-dimensional euclidean quantum gravity has been studied as a discrete model based on dynamical triangulations by Ambjorn and Jurkiewicz and by Agishtein and Migdal. We discuss a particular implementation of a Monte Carlo simulation of simplicial quantum gravity. As an application we introduce a non-uniform measure and examine its effect on simple aspects of the mathematical geometry. We find that the transition region from the hot to the cold phase is shifted and that the criticality of the transition changes.