Phase diagrams and multicritical points in randomly mixed magnets. II. Ferromagnet-antiferromagnet alloys.

The phase diagrams and critical behavior of a quenched random alloy of a ferromagnet and an antiferromagnet (or of two antiferromagnets with different periodicities) are studied in the mean-field approximation and by renormalization-group techniques. The antiferromagnetic order parameters are transformed into combinations of ferromagnetic order parameters, in order to study the possibility that ferromagnetic and antiferromagnetic orderings will become critical simultaneously. Averaging over the random variables yields a translationally invariant effective Hamiltonian, in which the $m$-component order parameters are replaced by $\mathrm{nm}$-component order parameters and the limit $n\to 0$ is taken in the end of the calculation. The phase diagram in the concentration-temperature plane is obtained in the mean-field approximation, and the nature of the ordered phases is discussed. In addition to the ordered phases of the pure ingredients, a mixed phase is sometimes found. For $m>\mathrm{}1\mathrm{}$, the ferromagnetic- and antiferromagnetic-order-parameter vectors are perpendicular to each other in this phase. The renormalization group is applied to study the multicritical point at which all these ordered phases meet. We don't find a stable fixed point appropriate for the description of this multicritical point. The physical implications of this fact are discussed. Finally, experiments on random alloys are reviewed and problems that should be studied experimentally are raised.