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)?

  • $\begingroup$ 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). $\endgroup$ – genneth Jan 17 '12 at 14:50
  • $\begingroup$ @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. $\endgroup$ – Space boy Jan 17 '12 at 15:41
  • $\begingroup$ The fixed point can be at small coupling, like large N. $\endgroup$ – Ron Maimon Jan 17 '12 at 16:51
  • $\begingroup$ @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? $\endgroup$ – Space boy Jan 17 '12 at 17:29
  • $\begingroup$ @Space boy: be patient, real answers will come. The comments are just off the cuff. $\endgroup$ – Ron Maimon Jan 17 '12 at 21:53

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