Faculty of Engineering, Shibaura Institute of Technology, 307 Fukasaku, Minuma, Saitama 337-8570, Japan.
Phys Rev E. 2019 Feb;99(2-1):023301. doi: 10.1103/PhysRevE.99.023301.
A spin-glass transition has been investigated for a long time but we have not reached a conclusion yet due to difficulties in the simulation studies. They are slow dynamics, strong finite-size effects, and sample-to-sample dependencies. We found that a size of the spin-glass order reaches a lattice boundary within a very short Monte Carlo step. A competition between the spin-glass order and a boundary condition causes these difficulties. Once the boundary effect was removed, physical quantities exhibited quite normal behaviors. They became self-averaging in a limit of large replica numbers. These findings suggest that the nonequilibrium relaxation method is a good choice for solving the difficulties if a lattice size and a replica number are set sufficiently large. A dynamic scaling analysis on nonequilibrium relaxation functions gave a result that the spin-glass transition and the chiral-glass transition occurs at the same temperature in the Heisenberg model in three dimensions. The estimated critical exponent ν agrees with the experimental result.
自旋玻璃转变已经研究了很长时间，但由于模拟研究中的困难，我们尚未得出结论。这些困难包括缓慢的动力学、强烈的有限尺寸效应和样本间的依赖性。我们发现，自旋玻璃有序的大小在非常短的蒙特卡罗步内达到晶格边界。自旋玻璃有序和边界条件之间的竞争导致了这些困难。一旦消除了边界效应，物理量就表现出相当正常的行为。在大量副本数量的限制下，它们变得自我平均。这些发现表明，如果晶格尺寸和副本数量设置得足够大，那么非平衡弛豫方法是解决这些困难的一个很好的选择。对非平衡弛豫函数的动态标度分析给出了一个结果，即在三维海森堡模型中，自旋玻璃转变和手性玻璃转变发生在相同的温度。估计的临界指数 ν 与实验结果一致。
