Infrared fixed point
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In physics, an infrared fixed point is a scale-invariant theory (fixed point) obtained by probing the very long-distance behavior of a quantum field theory or a model of statistical mechanics, as explained in the theory of the renormalization group.
This is a conformal field theory. One way, but certainly by far not the only way to get an IR fixed point is from second order phase transitions. Most infrared fixed points are trivial, aka Gaussian meaning that they describe massless free fields, but some, like the Banks-Zaks fixed point are nontrivial.