  We perform Monte Carlo simulations of 2-d dynamically triangulated surfaces
coupled to Ising and three--states Potts model matter. By measuring spin-spin
correlation functions as a function of the geodesic distance we provide
substantial evidence for a diverging correlation length at $\beta_c$. The
corresponding scaling exponents are directly related to the KPZ exponents of
the matter fields as conjectured in [4] (NPB454(1995)313).

High Energy Physics - Lattice