  We discuss the concept of connected, reparameterization invariant matter
correlators in quantum gravity. We analyze the effect of discretization in two
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-size effect and
propose an improved definition of the connected correlator, which 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 lattice in an external
magnetic field $H$, when $H \to 0$ and $\beta=\beta_C$.
