The Hausdorff dimension in polymerized quantum gravity

Abstract

We calculate the Hausdorff dimension, $d_H$, and the correlation function exponent, $η$, for polymerized two dimensional quantum gravity models. If the non-polymerized model has correlation function exponent $η_0 >3$ then $d_H=γ^{-1}$ where $γ$ is the susceptibility exponent. This suggests that these models may be in the same universality class as certain non-generic branched polymer models.