Renormalisation group - Which critical points are usefull in a RG flow diagram?

[IFNT]

In a RG flow diagram for a physical system where we have two fix points, which one is the most important one and describes the physical theory of the system?
Is it the unstable fix point or the "stable" one where some of the flow lines flows towards?

 

[Avodyne]

It depends on what physical question you want to ask.

Take QCD as an example. To describe high-energy scattering processes, we calculate near the UV fixed point. To describe the low-energy hadron spectrum, we calculate (via monte carlo simulations in lattice gauge theory) near the IR fixed point.