A zero of the beta function approached by the running coupling as the energy scale increases. A simple one-coupling fixed point with attracts nearby flows. Such a point can control two-point scaling at an ultraviolet fixed point.
If , and the reference correlator has a finite nonzero fixed-point limit, the characteristic solution of the multiplicative Callan-Symanzik equation gives . A simple attractive fixed point and smooth anomalous dimension give a finite prefactor multiplying . A nonsimple fixed point can retain slower corrections.
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The term "ultraviolet fixed point" often arises in the context of quantum field theory, statistical mechanics, and other areas of theoretical physics. In general, a **fixed point** refers to a set of parameters in a theory (such as coupling constants) for which the behavior of the system does not change under changes in the scale (i.e., under renormalization group transformations). The scale could be related to energy, temperature, or other physical dimensions.