论文标题
人口退火的加权平均值：分析和一般框架
Weighted averages in population annealing: analysis and general framework
论文作者
论文摘要
人口退火是一种强大的顺序蒙特卡洛算法，旨在通过大规模的并行性研究统计物理中通用系统的平衡行为。除了该方法的显着缩放功能外，它还可以通过平均加权来增强测量值，并承认基于独立重复的模拟来减少系统和统计错误。我们通过加权平均进行自我介绍，对人口退火，将方法概括为多种可观察物，例如特定的热量和磁化敏感性，并严格地证明，有限系统的最终估计量是渐近地公正的，以实质上是任意任意的目标分布。基于二维Ising Ferromagnet和Edwards-Anderson Ising Spin Glass的$ 10^7 $独立人口退火运行的数值结果。在后一种情况下，我们还讨论了测量人口退火模拟中旋转重叠的有效方法。
Population annealing is a powerful sequential Monte Carlo algorithm designed to study the equilibrium behavior of general systems in statistical physics through massive parallelism. In addition to the remarkable scaling capabilities of the method, it allows for measurements to be enhanced by weighted averaging, admitting to reduce both systematic and statistical errors based on independently repeated simulations. We give a self-contained introduction to population annealing with weighted averaging, generalize the method to a wide range of observables such as the specific heat and magnetic susceptibility and rigorously prove that the resulting estimators for finite systems are asymptotically unbiased for essentially arbitrary target distributions. Numerical results based on more than $10^7$ independent population annealing runs of the two-dimensional Ising ferromagnet and the Edwards-Anderson Ising spin glass are presented in depth. In the latter case, we also discuss efficient ways of measuring spin overlaps in population annealing simulations.
