带最佳估计的蒙特卡罗循环法：应用于合金自由能计算
Waste-recycling Monte Carlo with optimal estimates: application to free energy calculations in alloys
摘要：
最近提出的估计量Delmas和Eddain废物回收蒙特卡罗实现方差最佳减少相对于一个控制变量，直接使用模拟数据进行评估。在这里，这个估计的性能进行评估数值计算的自由能在一般的二元合金，并比较从文献中采取的其他估计。本文首先采用路径采样方法对一个简化的反铁磁伊辛模型系统进行了系统的研究。我们观察到数字（i）的Delmas-Escherdain估计量的方差确实减少相比，其他估计量;和（ii）由此产生的减少是接近最大可能的，尽管在估计的控制变量的不准确性。更广泛的路径采样模拟涉及的FeCr合金系统所描述的多体势另外表明，（iii）逐渐嬗变容纳原子的挫折，从而减轻了数值遍历性问题存在于众多的合金系统，并最终使相共存条件的确定。
英文摘要：
The estimator proposed recently by Delmas and Jourdain for waste-recycling Monte Carlo achieves variance reduction optimally with respect to a control variate that is evaluated directly using the simulation data. Here, the performance of this estimator is assessed numerically for free energy calculations in generic binary alloys and compared to those of other estimators taken from the literature. A systematic investigation with varying simulation parameters of a simplified system, the anti-ferromagnetic Ising model, is first carried out in the transmutation ensemble using path-sampling. We observe numerically that (i) the variance of the Delmas-Jourdain estimator is indeed reduced compared to that of other estimators; and that (ii) the resulting reduction is close to the maximal possible one, despite the inaccuracy in the estimated control variate. More extensive path-sampling simulations involving a FeCr alloy system described by a many-body potential additionally show that (iii) gradual transmutations accommodate the atomic frustrations, thus alleviating the numerical ergodicity issue present in numerous alloy systems and eventually enabling the determination of phase coexistence conditions.
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