FINITE-SIZE EFFECTS FOR THE ISING-MODEL COUPLED TO 2-D RANDOM SURFACES

Finite size effects for the Ising Model coupled to two-dimensional ran dom surfaces are studied by exploiting the exact results from the 2-ma trix models. The fixed area partition function is numerically calculat ed with arbitrary precision by developing an efficient algorithm for r ecursively solving the quintic equations so encountered. An analytic m ethod for studying finite size effects is developed based on the behav iour of the free energy near its singular points. The generic form of finite size corrections so obtained are seen to be quite different fro m the phenomenological parameterisations used in the literature. The m ethod of singularities is also applied to study the magnetic susceptib ility, A brief discussion is presented on the implications of these re sults to the problem of a reliable determination of string susceptibil ity from numerical simulations.