经典正则系统平行回火抽样的不完全β函数律
The incomplete beta function law for parallel tempering sampling of classical canonical systems
摘要：
我们表明，接受概率互换的并行回火蒙特卡罗方法的经典正则系统是由一个通用的功能，取决于平均统计波动的潜力和温度的比率。该定律被称为不完全贝塔函数定律，在交换中涉及的两个温度彼此接近的限制下有效。经验版本的法律，其中涉及的系统的热容量，开发和测试的Lennard-Jones集群。我们认为，平行回火的中间温度的分布的最佳初始猜测是一个几何级数，我们还提出了一种技术的计算最佳温度计划。最后，我们证明了交换效率的并行回火方法的凝聚相系统自然下降到零至少一样快的物理系统的维数的平方根倒数。
英文摘要：
We show that the acceptance probability for swaps in the parallel tempering Monte Carlo method for classical canonical systems is given by a universal function that depends on the average statistical fluctuations of the potential and on the ratio of the temperatures. The law, called the incomplete beta function law, is valid in the limit that the two temperatures involved in swaps are close to one another. An empirical version of the law, which involves the heat capacity of the system, is developed and tested on a Lennard-Jones cluster. We argue that the best initial guess for the distribution of intermediate temperatures for parallel tempering is a geometric progression and we also propose a technique for the computation of optimal temperature schedules. Finally, we demonstrate that the swap efficiency of the parallel tempering method for condensed-phase systems decreases naturally to zero at least as fast as the inverse square root of the dimensionality of the physical system.
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