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**what does "mixing under RG flow" mean?**

I'm trying to understand the language people use when they talk about RG flow. Here's what I understand:

We have the RG flow equations governing the couplings' dependence on energy scale

[tex]\mu {dg_i \over d\mu}=\beta(g_j)[\tex],

and we can find the "fixed points" by solving

[tex]\beta(g_j)[\tex]=0[\tex].

We can linearize to find "stable" and "unstable" trajectories in coupling space, emerging from these fixed points.

What I'm not so sure of is what "RG flow" means. I'm guessing that if we move away from the fixed point, then vary the energy scale, we will move along whatever trajectory we are sitting on. Is this what RG flow means?

My real question is this: What does it mean for two operators to "mix under RG flow"?

Thanks for any help.