Nonomura Yoshihiko, Tomita Yusuke
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 Stat Nonlin Soft Matter Phys. 2015 Dec;92(6):062121. doi: 10.1103/PhysRevE.92.062121. Epub 2015 Dec 10.
Recently we showed that the critical nonequilibrium relaxation in the Swendsen-Wang algorithm is widely described by the stretched-exponential relaxation of physical quantities in the Ising or Heisenberg models. Here we make a similar analysis in the Berezinsky-Kosterlitz-Thouless phase transition in the two-dimensional (2D) XY model and in the first-order phase transition in the 2D q=5 Potts model and find that these phase transitions are described by the simple exponential relaxation and power-law relaxation of physical quantities, respectively. We compare the relaxation behaviors of these phase transitions with those of the second-order phase transition in the three- and four-dimensional XY models and in the 2D q-state Potts models for 2≤q≤4 and show that the species of phase transitions can be clearly characterized by the present analysis. We also compare the size dependence of relaxation behaviors of the first-order phase transition in the 2D q=5 and 6 Potts models and propose a quantitative criterion on "weakness" of the first-order phase transition.
最近我们表明，斯温森 - 王算法中的临界非平衡弛豫在很大程度上由伊辛模型或海森堡模型中物理量的拉伸指数弛豫来描述。在此，我们对二维（2D）XY模型中的贝雷津斯基 - 科斯特利茨 - Thouless相变以及二维q = 5 Potts模型中的一阶相变进行了类似分析，发现这些相变分别由物理量的简单指数弛豫和幂律弛豫来描述。我们将这些相变的弛豫行为与三维和四维XY模型以及2≤q≤4的二维q态Potts模型中的二阶相变的弛豫行为进行了比较，结果表明，通过当前分析可以清晰地表征相变的类型。我们还比较了二维q = 5和6 Potts模型中一阶相变弛豫行为的尺寸依赖性，并提出了关于一阶相变“弱点”的定量判据。
