Swendsen-Wang算法中Berezinsky-Kosterlitz-弱一级相变的临界非平衡弛豫
Critical nonequilibrium relaxation in the Swendsen-Wang algorithm in the Berezinsky-Kosterlitz-Thouless and weak first-order phase transitions
摘要：
最近，我们证明了Swendsen-Wang算法中的临界非平衡弛豫可以用Ising或Heisenberg模型中的物理量的拉伸指数弛豫来描述。本文对二维XY模型中的Berezinsky-Kosterlitz无相变和二维$q=5$ Potts模型中的一级相变进行了类似的分析，发现这些相变分别可用物理量的简单指数松弛和幂律松弛来描述。我们比较了这些相变的弛豫行为与三维和四维XY模型中的二级相变和二维$q$ -态Potts模型中的$2 \le q \le 4$的二级相变的弛豫行为，并表明本分析可以清楚地表征相变的种类。我们还比较了二维$q=5$和$6$ Potts模型中一级相变弛豫行为的尺寸依赖性，并提出了一个一级相变“弱”的定量判据.
英文摘要：
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 3D and 4D XY models and in the 2D $q$-state Potts models for $2 \le q \le 4$, 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.
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