Heisenberg spin glasses with a strong random anisotropy

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We have studied the phase transition of the ±J Heisenberg model in three dimensions. Using the exchange Monte Cairo method, we have investigated the spin-overlap distribution near the SG transition temperature. By selecting the order parameter as the maximum value of the spin overlap of the diagonal componentsunder the uniform rotations, the calculated overlap distribution suggests the appearance of a peculiar type of replica-symmetry breaking which is similar to the one found in the chirality-overlap distribution by Hukushima and Kawamura. This result may explain absence of any crossing of the Binder parameter of the spin at a finite SG transition temperature.We have also studied the ground state and low-lying excitations of the ±J Heisenberg model on a three dimensional L×L×L (L≦11) lattice. We found evidence of occurrence of a Parisi state. That is, there exists a metastable state with a finite energy of ΔE〜O(J) in the thermodynamic limit and the energy barrier ΔW between the metastable state and the ground state is ΔW∝JL^θ with θ〜0.53. We also found that the energy ΔE of small scale excitations are related to a scale of the excitation V in a similar manner to those of the ferromagnetic model, i. e., ΔE∝J L^ΦV^Ψ with Φ〜-4.7 and Ψ〜2.0. This fact suggests that similarity exists in the ground state structure between the ±J and the ferromagnetic Heisenberg models, though the spin directions of those two models differ greatly from one another.