The Banks–Zaks fixed point is a concept in quantum field theory and statistical physics, particularly in the study of quantum phase transitions and the behavior of gauge theories. It refers to a non-trivial fixed point in the renormalization group flow of certain quantum field theories, specifically the case of three-dimensional supersymmetric gauge theories or certain four-dimensional gauge theories with specific matter content.
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A non-Abelian gauge theory can have a weak infrared fixed point when the one-loop coefficient of its renormalization-group beta function is small and positive while the two-loop coefficient is negative. For and evolution in , has the displayed zero and slope . Fundamental-fermion flavor number just below the asymptotic-freedom boundary produces this regime.