Something to think about!

An effective field theory (EFT) is equivalent to a system of statistical mechanics close to a second order phase transition. The correlation functions in the EFT go like $e^{-m/\Lambda}$ and therefore the assumption of small masses in the EFT corresponds to the divergence of correlation functions in the Stat. Mech. system close to the continuous phase transition.
Think about this:
What is the meaning of a non-renomrmalizable EFT in the Stat. Mech.-EFT dictionary?