Correlators for the Complex Matrix Model

We describe an iterative scheme which allows us to calculate any multi-loop corre-lator for the complex matrix model to any genus using only the first in the chain of loop equations. The method works for a completely general potential and the results contain no explicit reference to the couplings. The genus g contribution to the m–loop correlator depends on a finite number of parameters, namely at most 4g − 2 + m. We find the generating functional explicitly up to genus three. We show as well that the model is equivalent to an external field problem for the complex matrix model with a logarithmic potential.