Critical behavior of amorphous magnets

Renormalization-group techniques are applied to a model Hamiltonian recently proposed by Harris, Plischke, and Zuckermann for the description of amorphous magnets. In this model, a single-ion uniaxial anisotropy, with a random direction of the axis of anisotropy, is introduced. Averaging over this random variable yields an (translationally invariant) effective Hamiltonian, in which the $m$-component spin variable is replaced by an $\mathrm{nm}$-component vector, and $n$ is finally set equal to zero. Contrary to the result for an isotropic random perturbation, the fixed-point describing the nonrandom $m$-component critical behavior is unstable with respect to terms in the Hamiltonian generated by the randomness, the appropriate crossover exponent being given exactly by ($2{\phi }_m-2+{\alpha }_m$), where ${\phi }_m$ is the Fisher-Pfeuty anisotropic spin crossover exponent and ${\alpha }_m$ is the specific-heat exponent. Depending on the distribution function for the random anisotropy directions, there are seven or thirteen other fixed points. Most of these are unstable, and the recursion relations probably yield a "runaway" which is interpreted as a smeared transition. Experiments on amorphous Tb${\mathrm{Fe}}_2$ are discussed.