PERTURBATIVE ANALYSIS OF AN N-ISING MODEL ON A RANDOM SURFACE

Two-dimensional quantum gravity coupled to a conformally invariant matter field of central charge c = 1/2 n, is represented, in a discretized version, by n independent Ising spins per cell of the triangulations of a random surface. The matrix integral representation of this modes leads to a diagrammatic expansion in powers of the cosmological constant for fixed genus. From the behaviour of this expansion at large orders, when the Ising coupling constant is tuned to criticality, one extracts the values of the string susceptibility exponent. We extend our previous calculation to order eight for genus zero and investigate now also the genus one case in order to check the possibility of having a well-defined double scaling limit even for c > 1.