  Within the framework of string field theory the intrinsic Hausdorff dimension
d_H of the ensemble of surfaces in two-dimensional quantum gravity has recently
been claimed to be 2m for the class of unitary minimal models (p = m+1,q = m).
This contradicts recent results from numerical simulations, which consistently
find d_H approximatly 4 in the cases m = 2, 3, 5 and infinity. The string field
calculations rely on identifying the scaling behavior of geodesic distance and
area with respect to a common length scale l. This length scale is introduced
by formulating the models on a disk with fixed boundary length l. In this paper
we study the relationship between the mean area and the boundary length for
pure gravity and the Ising model coupled to gravity. We discuss how this
relationship is modified by relevant perturbations in the Ising model. We
discuss how this leads to a modified value for the Hausdorff dimension.
