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Why are RG flow fixed points associated with different phases? I thought the RG makes only statements about behavior near to critical points... a definite phase is far away from the critical point, right?

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    $\begingroup$ What does the acronym RG stand for? $\endgroup$ – Ben Crowell Nov 14 '18 at 21:12
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RG fixed points themselves are not associated with phases. Rather, RG fixed points (and their basins of attraction) describe systems at a phase transition. You are correct that taking the limit as a system approaches the critical surface only allows us to make statements about the system near the transition, but the RG is also used more broadly. The different relevant perturbations of a fixed point describe the possible phases (low-energy behaviors). By tuning the relevant perturbations to zero, we reach criticality, e.g. phase transitions.

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