National Research University Higher School of Economics, 101000 Moscow, Russia.
Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany.
Phys Rev E. 2019 Dec;100(6-1):063303. doi: 10.1103/PhysRevE.100.063303.
We study properties of Markov chain Monte Carlo simulations of classical spin models with local updates. We derive analytic expressions for the mean value of the acceptance rate of single-spin-flip algorithms for the one-dimensional Ising model. We find that for the Metropolis algorithm the average acceptance rate is a linear function of energy. We further provide numerical results for the energy dependence of the average acceptance rate for the three- and four-state Potts model, and the XY model in one and two spatial dimensions. In all cases, the acceptance rate is an almost linear function of the energy in the critical region. The variance of the acceptance rate is studied as a function of the specific heat. While the specific heat develops a singularity in the vicinity of a phase transition, the variance of the acceptance rate stays finite.
我们研究了具有局部更新的经典自旋模型的马尔可夫链蒙特卡罗模拟的性质。我们推导出了一维伊辛模型中单自旋翻转算法的接受率平均值的解析表达式。我们发现，对于 Metropolis 算法，平均接受率是能量的线性函数。我们进一步提供了三态和四态 Potts 模型以及一维和二维 XY 模型中平均接受率对能量的依赖关系的数值结果。在所有情况下，在临界区域中，接受率几乎是能量的线性函数。我们还研究了接受率的方差作为比热的函数。虽然比热在相变附近出现奇点，但接受率的方差仍保持有限。
