Symmetry breaking ’’irrelevant’’ operators and tetracritical points in anisotropic magnets

The phase diagram of a cubic magnet, with a variable uniaxial anisotropy, is studied. For a range of values of the cubic anisotropy energy, it exhibits a tetracritical point, at which three ordered phases and the disordered phase coexist. These are separated by four second‐order lines. The shapes of these lines, as functions of the uniaxial anisotropy, are calculated using scaling arguments and expansions in ε=4‐d and in 1/n.