Asymptotic graph counting techniques in ψ2N field theory

We discuss two different techniques for obtaining asymptotic estimates of the number of n-vertex graphs in a ψ2N field theory as n→∞. The first technique relies on difference equations and the second makes use of Lipatov’s methods. We show how various topological constraints, such as connectedness and Wick ordering, affect the total number of graphs. We show, for example, that Wick ordering reduces the total number of connected graphs by a factor of eN−1/2 as n→∞.