Effects of anisotropy on a quantum Heisenberg spin glass in a three-dimensional hierarchical lattice

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We study the anisotropic Heisenberg spin-glass model in a three-dimensional hierarchical lattice (designed to approximate the cubic lattice), within a real-space renormalization-group approach. Two different initial probability distributions for the exchange interaction (Jij), Gaussian and uniform, are used, with zero mean and width J. The (kT/J) × Δ₀ phase diagram is obtained, where T is the temperature, Δ₀ is the first moment of the probability distribution for the uniaxial anisotropy, and k is the Boltzmann constant. For the Ising model (Δ₀=1), there is a spin-glass phase at low temperatures (high J) and a paramagnetic phase at high temperatures (low J). For the isotropic Heisenberg model (Δ₀=0), our results indicate no spin-glass phase at finite temperatures. The transition temperature between the spin-glass and paramagnetic phase decreases with Δ₀, as expected, but goes to zero at a finite value of the anisotropy parameter, namely Δ₀ = Δc 0.59. Our results indicate that the whole transition line, between the paramagnetic and the spin-glass phases, for Δc ≤ Δ₀ < 1, belongs to the same universality class as the transition for the Ising spin glass.