EDF-R&D, Département Matériaux et Mécanique des Composants, Les Renardières, 77818 Moret-sur-Loing, France.
J Chem Phys. 2011 Jul 28;135(4):044127. doi: 10.1063/1.3610423.
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 is 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 an 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.
德尔马斯和茹尔丹最近提出的废物循环蒙特卡罗估算器，通过使用模拟数据直接评估的控制变量，针对其进行了最优的方差减少。在此，针对通用二进制合金中的自由能计算，对该估算器的性能进行了数值评估，并与文献中其他估算器进行了比较。首先，在转变系综中，使用路径抽样对简化系统（反铁磁伊辛模型）进行了随模拟参数变化的系统研究。我们从数值上观察到：（i）与其他估算器相比，德尔马斯-茹尔丹估算器的方差确实降低了；并且（ii）尽管估计的控制变量存在误差，但降低的幅度接近最大可能值。涉及由多体势描述的 FeCr 合金系统的更广泛的路径抽样模拟还表明：（iii）逐渐的转变适应了原子的挫折感；从而减轻了在许多合金系统中存在的数值遍历性问题，并最终能够确定相共存条件。
