Critical behaviour of correlation functions in scaler field theories

From the Mellin representation for Feynman integrals, an asymptotic expansi on for a generic Feynman amplitude, for any set of invariants going to zero or to infinity, can be obtained. If we take all masses going to zero in Eu clidean metric, the truncated expansion has a rest compatible with converge nce of the series. In the spirit of the application of field theory to crit ical phenomena, we consider from our general asymptotic expansions the crit ical behaviour of correlation functions. In particular, we perform a detail ed analysis of the critical behaviour of the two-point correlation function in terms of Feynman graphs. (C) 2001 Elsevier Science B.V. All rights rese rved.