Absence of Spin Glass Ordering in Some Random Spin Systems

We discuss the improvement of the imperfect argument of Schuster for the absence of spin glass ordering at and below four dimensions in short-range continuous spin systems, and propose a condition for his method to be justified. Assuming satisfaction of the above condition, we apply the method to long-range interactions to reproduce the phase diagram drawn by a renormalization group approach. In particular the three-dimensional RKKY system is found to be at the lower critical dimension. Effects of exchange and uniaxial anisotropics are discussed. The latter anisotropy is shown not to induce transverse spin glass ordering if the system is not ordered in the xy-plane by the exchange interaction.