An approximation for random surfaces on arbitrary target spaces

A perturbative technique, the low-temperature expansion, is developed for matrix models of random surfaces. It can be applied to models with arbitrary target spaces, including ones with c>1. As a simple illustration, the series is worked out to 10th order for the surface coupled to a q-state Potts model. Accurate estimates for, e.g., $\gamma_{str}$ are obtained both in the low q (c<1) and high q (branched polymer) regimes, including the logarithmic corrections to scaling.