Spin-spin correlation functions of spin systems coupled to 2-d quantum gravity for $0<c<1$

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).