The Hausdorff dimension in polymerized quantum gravity

TL;DR

This paper computes the Hausdorff dimension and correlation function exponent for polymerized 2D quantum gravity models, revealing potential universality with branched polymer models.

Contribution

It introduces calculations of geometric and correlation exponents in polymerized quantum gravity, linking them to known universality classes.

Findings

If the non-polymerized model has η₀ > 3, then d_H = γ^{-1}.

Polymerized models may belong to the same universality class as certain branched polymers.

The study provides a connection between quantum gravity models and polymer universality classes.

Abstract

We calculate the Hausdorff dimension, $d_H$, and the correlation function exponent, $\eta$, for polymerized two dimensional quantum gravity models. If the non-polymerized model has correlation function exponent $\eta_0 >3$ then $d_H=\gamma^{-1}$ where $\gamma$ is the susceptibility exponent. This suggests that these models may be in the same universality class as certain non-generic branched polymer models.