Volume dependence of the phase boundary in 4D dynamical triangulation

TL;DR

This paper investigates how the phase boundary in 4D dynamical triangulation models depends on volume, suggesting a potential scaling region where the system's behavior could differ from the crumpled phase at large volumes.

Contribution

It explores the volume dependence of the phase boundary in 4D dynamical triangulation, proposing a scaling region where the system may avoid the crumpled phase.

Findings

Number of configurations grows faster than exponentially with volume

A scaling region exists where $ abla_2$ can go to infinity with volume

Implication that phase behavior may differ at large volumes

Abstract

The number of configurations of the dynamical triangulation model of 4D euclidean quantum gravity appears to grow faster than exponentially with the volume, with the implication that the system would end up in the crumpled phase for any fixed $\kappa_2$ (inverse bare Newton constant). However, a scaling region is not excluded if we allow $\kappa_2$ to go to infinity together with the volume.