Renormalized Field Theory of Random Magnetic Mixtures with Competing Spin Anisotropies. I

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Abstract
Non-symmetric multicritical points in random magnetic mixtures with competing spin anisotropies are studied by means of the renormalized field theory and the replica method. Nine β functions and two critical indices η are evaluated up to O(ε2)[ε=4-d(d: space dimensionality)]. The investigated model consists of two terms: the anisotropic exchange energy previously studied by Fishman-Aharony and the random off-diagonal anisotropy energy (RAM) recently proposed by Mukamel-Grinstein. Many randomly mixed magnets have the latter term due to the spin lattice coupling or the dipole-dipole interaction. Random off-diagonal anisotropy energy couples longitudinal and transverse spin components in this system. Owing to the existence of this term, the second-order tetracritical point predicted by Fishman-Aharony should be replaced by the unstable coupled tetracritical point, which corresponds to the first-order or smeared phase transition.

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