John Wheater

Abstract:

We describe a simple lattice model of higher-curvature quantum gravity in two dimensions and study the phase structure of the theory as a function of the curvature coupling. It is shown that the ensemble of flat graphs is entropically unstable to the formation of baby universes. In these simplified models the growth in graphs exhibits a branched polymer behaviour in the phase directly before the flattening transition.

Abstract:

We show that the spectral dimension on non-generic branched polymers with susceptibility exponent gamma > 0 is given by d(s) = 2/(1 + gamma). For those models with gamma < 0 we find that d(s) = 2.

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.