Self-consistent nonperturbative anomalous dimensions

A self-consistent treatment of two- and three-point functions in models with trilinear interactions forces them to have opposite anomalous dimensions. We indicate how the anomalous dimension can be extracted nonperturbatively by solving and suitably truncating the topologies of the full Dyson-Schwinger set of equations. The first step requires a sensible ansatz for the full vertex part, which conforms to first order perturbation theory at least. We model this vertex to obtain typical transcendental relations between anomalous dimension and coupling constant g which coincide with known results to order g 4.