theta vacuum: A matrix model

We model the effects of a large number of zero modes for N-f species of qua rks at finite vacuum angle theta, using a matrix model with Gaussian weight s constrained by the topological susceptibility and compressibility. The qu enched free energy exhibits a cusp at theta < <pi> that is sensitive to the accuracy of the numerical analysis and the maximum density of winding mode s. Our results bear much in common with recent lattice simulations by Schie rholz and others. The unquenched free energy exhibits similar sensitivities , but for small quark masses or a large density of zero modes the results a re in agreement with those derived using anomalous Ward identities and effe ctive Lagrangians.