Breakdown of universality in multi-cut matrix models

We solve the puzzle of the disagreement between orthogonal polynomials meth ods and mean-field calculations for random N x N matrices with a disconnect ed eigenvalue support. We show that the difference does not stem from a Z(2 ) symmetry breaking, but from the discreteness of the number of eigenvalues . This leads to additional terms (quasiperiodic in N) which must be added t o the naive mean-field expressions. Our result invalidates the existence of a smooth topological large-N expansion and some postulated universality pr operties of correlators. We derive the large N expansion of the free energy for the general two-cut case. From it we rederive by a direct and easy mea n-field-like method the two-point correlators and the asymptotic orthogonal polynomials. We extend our results to any number of cuts and to non-real p otentials.