We argue that when a short-range spin-glass system is below its lower critical dimension dₗ, which seems to be the case for isotropic vector spins in three dimensions, then the corresponding Ruderman-Kittel-Kasuya-Yosida (RKKY) system is in a different universality class and at its lower critical dimension. For dimensions greater than dₗ, the RKKY and short-range systems have the same critical behavior. This appears to apply to Ising spins, and to anisotropic vector-spin models for which we discuss the dependence of Tc on anisotropy.
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Bray et al. (1986) studied this question.
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