Landau Institute for Theoretical Physics, 142432 Chernogolovka, Russia.
Science Center in Chernogolovka, 142432 Chernogolovka, Russia.
Phys Rev E. 2017 Oct;96(4-1):043307. doi: 10.1103/PhysRevE.96.043307. Epub 2017 Oct 18.
The Wang-Landau (WL) algorithm has been widely used for simulations in many areas of physics. Our analysis of the WL algorithm explains its properties and shows that the difference of the largest eigenvalue of the transition matrix in the energy space from unity can be used to control the accuracy of estimating the density of states. Analytic expressions for the matrix elements are given in the case of the one-dimensional Ising model. The proposed method is further confirmed by numerical results for the one-dimensional and two-dimensional Ising models and also the two-dimensional Potts model.
Wang-Landau（WL）算法已广泛应用于物理学的许多领域的模拟中。我们对 WL 算法的分析解释了其性质，并表明可以使用能量空间中转移矩阵的最大特征值与 1 的差值来控制估计态密度的精度。在一维伊辛模型的情况下给出了矩阵元的解析表达式。一维和二维伊辛模型以及二维 Potts 模型的数值结果进一步证实了所提出的方法。
