The Hausdorff dimension in polymerized quantum gravity

We calculate the Hausdorff dimension, dH, and the correlation function exponent, η, for polymerized two dimensional quantum gravity models. If the non-polymerized model has correlation function exponent η0>3 then dH=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.