Heisenberg spin glasses with a strong random anisotropy

我们从三维角度研究了±J海森堡模型的相变。用交换蒙特卡罗方法研究了SG相变温度附近的自旋重叠分布。通过选取序参数作为均匀旋转下对角分量自旋重叠的最大值，计算的重叠分布表明出现了一种特殊类型的复制对称破缺，它类似于Hukushima和Kawamura在手性重叠分布中发现的类型。这一结果可以解释在有限的SG转变温度下自旋的键参数不存在任何交叉。我们还研究了三维L×L×L(L≦11)晶格上±J海森堡模型的基态和低激发态。我们发现了巴黎国家出现的证据。也就是说，在热力学极限下，存在一个能量有限的亚稳态ΔE~O(J)，介稳和基态之间的势垒ΔW是ΔW∝JL？θ，θ~0.53。我们还发现，小尺度激发的能量ΔE与激发尺度V的关系与铁磁模型相似，即ΔE∝J L？ΦV^Ψ，Φ~-4.7和Ψ~2.这一事实表明，尽管±J模型和铁磁Heisenberg模型的自旋方向有很大的不同，但这两个模型的基态结构存在相似性。

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.