Computational Materials Science Unit, National Institute for Materials Science, Tsukuba, Ibaraki 305-0044, Japan.
College of Engineering, Shibaura Institute of Technology, Saitama 337-8570, Japan.
Phys Rev E. 2016 Jan;93(1):012101. doi: 10.1103/PhysRevE.93.012101. Epub 2016 Jan 4.
Recently, it was shown [Y. Nonomura, J. Phys. Soc. Jpn. 83, 113001 (2014)JUPSAU0031-901510.7566/JPSJ.83.113001] that the nonequilibrium critical relaxation of the two-dimensional (2D) Ising model from a perfectly ordered state in the Wolff algorithm is described by stretched-exponential decay, and a universal scaling scheme was found to connect nonequilibrium and equilibrium behaviors. In the present study we extend these findings to vector spin models, and the 3D Heisenberg model could be a typical example. To evaluate the critical temperature and critical exponents precisely using the above scaling scheme, we calculate nonequilibrium ordering from the perfectly disordered state in the Swendsen-Wang algorithm, and we find that the critical ordering process is described by stretched-exponential growth with a comparable exponent to that of the 3D XY model. The critical exponents evaluated in the present study are consistent with those in previous studies.
最近，人们已经表明[Y. Nonomura, J. Phys. Soc. Jpn. 83, 113001 (2014)JUPSAU0031-901510.7566/JPSJ.83.113001]，在 Wolff 算法中，从完美有序状态出发的二维（2D）伊辛模型的非平衡临界弛豫可以用拉伸指数衰减来描述，并且发现了一个通用的标度方案来连接非平衡和平衡行为。在本研究中，我们将这些发现扩展到了矢量自旋模型，而 3D 海森堡模型可能是一个典型的例子。为了使用上述标度方案精确地评估临界温度和临界指数，我们在 Swendsen-Wang 算法中从完全无序状态计算了非平衡排序，并且我们发现临界排序过程可以用拉伸指数增长来描述，其指数与 3D XY 模型的指数相当。本研究中评估的临界指数与先前研究中的一致。
