Theoretical Investigations on the spin-glass phase transitions and its low-temperature phase using the nonequilibrium relaxation method

本研究项目的目的是在三维空间阐明海森堡自旋玻璃模型中的自旋玻璃跃迁。为了深入理解SG相变和低温相，我们还研究了XY模型和Ising模型。我们的主要结果如下：开发有效的数值配方：为了提高有限时间尺度分析的准确性，我们开发了各种方案。海森堡SG模型中自旋和手性玻璃化转变的三维解析：手性玻璃化转变发生在比自旋玻璃化转变温度更高的温度下。我们还观察到，自旋和手性在SG转变温度以上解耦，在SG转变温度以下耦合。动态普适性：我们发现了三维自旋玻璃跃迁和手性玻璃跃迁存在动态普适性的可能性。所有研究的相变都表现出相同的动态临界指数。SG相中低温交叉：我们发现自旋玻璃相中存在交叉温度，基态松弛出现。低于此交叉温度的动态行为相当于T=0动态。还估计了基态的动态指数。在伊辛模型和海森堡模型之间，它的值几乎相同。量子自旋玻璃问题的准备：我们研究了随机交替量子自旋链的量子相变。我们开发的方法被证实适用于这一有趣的问题。

The aim of this research project is to clarify the spin-glass (SG) transition in the Heisenberg spin-glass model in three dimensions. In order to achieve thorough understandings of the SG transition and the low-temperature phase, we also investigated the XY model and the Ising model. Our main results are as follows.1.Development of efficient numerical recipes : We developed various protocols of the finite-time scaling analysis in order to improve the accuracy.2.Resolution of the spin- and the chiral-glass transitions in the Heisenberg SG model in three dimensions : The chiral-glass transition is confirmed to occur at higher temperature than the spin-glass transition temperature. We also observed that the spin and the chirality are decoupled above the SG transition temperature and become coupled below it.3.Dynamic universality : We found a possibility of the dynamic universality in the spin- and the chiral-glass transitions in three dimensions. All the investigated phase transition exhibit the same dynamic critical exponent.4.Low-temperature crossover in the SG phase : We found a crossover temperature in the spin-glass phase, where the ground-state relaxation appears. The dynamic behavior below this crossover temperature is equivalent to the T=0 dynamics. A dynamic exponent of the ground state is also estimated. It takes almost the same value between the Ising model and the Heisenberg model.5.Preparation for the quantum spin-glass problems : We investigated the quantum phase transition of the random alternating quantum spin chain. Our developed method is confirmed to be applicable to this interesting problems.