Critical behaviour of correlation functions in scalar field theories

From the Mellin representation for Feynman integrals, an asymptotic expansion for a generic Feynman amplitude, for any set of invariants going to zero or to ∞, can be obtained. If we take all masses going to zero in Euclidean metric, the truncated expansion has a rest compatible with convergence of the series. In the spirit of the application of field theory to critical phenomena, we consider from our general asymptotic expansions the critical behaviour of correlation functions. In particular, we perform a detailed analysis of the critical behaviour of the two-point correlation function in terms of Feynman graphs.