Connected correlators in quantum gravity

We discuss the concept of connected, reparameterization invariant matter co rrelators in quantum gravity. We analyze the effect of discretization in tw o solvable cases: branched polymers and two-dimensional simplicial gravity. In both cases the naively defined connected correlators for a fixed volume display an anomalous behavior, which could be interpreted as a long-range order. We suggest that this is in fact only a highly non-trivial finite-siz e effect and propose an improved definition of the connected correlator, wh ich reduces the effect. Using this definition we illustrate the appearance of a long-range spin order in the Ising model on a two-dimensional random l attice in an external magnetic field H, when H --> 0 and beta = beta(C).