Structure of Low-Temperature Phase of a Heisenberg Spin-Glass

1.+/-J Heisenberg自旋玻璃模型的相变我们用两种Monte Carlo方法研究了+/-J Heisenberg模型的相变。在平衡模拟中，我们已经计算了自旋玻璃磁化率的各种尺寸的晶格和外推到一个无限的晶格使用有限尺寸的标度分析。结果表明，自旋玻璃极化率在有限温度Tc处发散。我们还通过非平衡弛豫模拟研究了自旋玻璃极化率在无限晶格上的增长，发现自旋玻璃极化率在相同的温度Tc下表现出临界行为。由此我们得出结论：+/-J海森堡模型中存在相变，并且该模型的低温相是自旋玻璃相。2.自旋玻璃相的性质我们发展了一种搜索海森堡自旋玻璃模型基态和亚稳态的强有力的遗传算法。利用该算法，我们已经检查了基态和低躺在不同尺寸的晶格亚稳态的模型，并发现Parisi状态中实现的模型。也就是说，有许多低的亚稳态，其能量几乎与基态能量相同，并且通过无限大的能量势垒与基态分离。我们还研究了附近的Prisistates的激发，并发现这些激发具有类似的纯铁磁模型的属性。在此基础上，我们认为海森堡模型的自旋玻璃相可以用无限程自旋玻璃模型中提出的复制对称破缺理论来描述.

1.Phase transition of the +/-J Heisenberg spin glass modelWe have investigate the phase transition of the +/-J Heisenberg model by means of two Monte Carlo simulations. In the equilibrium simulation, we have calculated a spin-glass susceptibility for various sizes of the lattice and extrapolated it to that for an infinite lattice using a finite size scaling analysis. The result has suggested that the spin-glass susceptibility diverges at a finite temperature Tc. We have also examined the growth of the spin-glass susceptibility on an infinite lattice by mean of a non-equilibrium relaxation simulation and found that the spin-glass susceptibility exhibits a critical behavior at the same temperature Tc. Thus we conclude that a phase transition occurs in the +/-J Heisenberg model and the low temperature phase of the model is a spin-glass phase.2.Nature of the spin-glass phaseWe have developed a powerfull genetic algorithm for searching for the ground state and metastable states of a Heisenberg spin-glass model. Using the algorithm, we have examined the ground state and low-lying metastable states of the model on various sizes of the lattice and found that Parisi states are realized in the model. That is, there are many low-lying metastable states whose energies are almost the same as the ground state energy and which are separated from the ground state by an infinitely large energy barrier. We have also examined excitations near the Prisistates and found that those excitations have properties similar to those of the pure ferromagnetic model. On the basis of those results, we have suggested that the spin-glass phase of the Heisenberg model is well described by a replica-symmetry-breaking theory which was proposed in the infinite-range spin-glass model.