Question about the perturbative renormalization group

I'm currently learning about the renormalization group (RG) in condensed matter physics and just want to clarify a couple of things:

When doing the RG transformation, there's a flow to a fixed point. A coupling constant is a relevant operator (or relevant coupling, depending on which book you look at) if it gets larger as the transformation continues, and flows towards the fixed point.

Have I understood that correctly?

If doing perturbative renormalization, is it right that if you have a relevant operator it is not possible to use that operator in a perturbative expansion because it's large once the transformations are done (even if it was small to start with - before the RG transformations were done)?

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Yes and yes. Though quite often people ignore convergence issues. For real problems, it's best to let nature/experiment decide whether a series converges rather than trying to prove it one way or the other (semi-tongue in cheek). –  genneth Jan 17 '12 at 14:50
@genneth Thank you. Any chance you could look at my other question on renormalization? - It's linked to this one, so I thought you might know the answer. –  Space boy Jan 17 '12 at 15:41
The fixed point can be at small coupling, like large N. –  Ron Maimon Jan 17 '12 at 16:51
@Ron Thank you, but I'm a beginner at this, and don't understand how your answer relates to my question - could you clarify what you mean? –  Space boy Jan 17 '12 at 17:29
@Space boy: be patient, real answers will come. The comments are just off the cuff. –  Ron Maimon Jan 17 '12 at 21:53