Renormalization-group techniques developed to analyze bicritical and tetracritical points, specifically in $n$-component antiferromagnetic systems, are presented in detail. The treatment yields a scaling description of the critical behavior of anisotropic antiferromagnets in both parallel and skew, uniform and staggered magnetic fields, in particular, the bicritical, spin-flop transition is discussed. For $n\le 3$ it is described by a stable, isotropic, Heisenberg-like fixed point. However for $n\ge 4$ a new biconical fixed point, with irrational $\epsilon$-expansion coefficients, becomes stable and describes tetracritical behavior. Special attention is given to the singular shape of the ($T,H$) phase boundaries for both isotropic and anisotropic antiferromagnets.

• Received 6 May 1975

DOI:https://doi.org/10.1103/PhysRevB.13.412