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从三维角度阐明海森堡自旋玻璃模型中的自旋玻璃相变。为了对SG相变和低温相有更深入的了解，我们还研究了XY模型和Ising模型。我们的主要结果如下：1.发展了有效的数值公式：为了提高精度，我们发展了各种有限时间标度分析协议。2.海森堡SG模型中自旋-玻璃相变和手性-玻璃相变的三维分辨率：手性-玻璃相变发生在高于自旋-玻璃相变温度的温度。我们还观察到自旋和手性在SG相变温度以上解耦，在此温度以下发生耦合。3.动力学普适性：我们发现了三维自旋和手性玻璃相变中存在动力学普适性的可能性。所有被研究的相变都表现出相同的动态临界指数。4.SG相的低温渡越：我们在自旋玻璃相中发现了一个渡越温度，在那里出现了基态弛豫。低于此交叉温度的动态行为相当于T=0的动态行为。还估算了基态的动态指数。Ising模型和Heisenberg模型具有几乎相同的值。5.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.