  We present a simple and consistent way to compute correlation functions in
interacting theories with non-trivial phase diagram. As an example we show how
to consistently compute the four-point function in three dimensional
$\mathbb{Z}_2$-scalar theories. The idea is to perform the path integral by
weighting the momentum modes that contribute to it according to their
renormalization group (RG) relevance, i.e. we weight each mode according to the
value of the running couplings at that scale. In this way, we are able encode
in a loop computation the information regarding the RG trajectory along which
we are integrating. We show that depending on the initial condition, or initial
point in the phase diagram, we obtain different behaviors of the four-point
function at the end point of the flow.
