蒙特卡罗模拟中遍历性的探讨
The Approach to Ergodicity in Monte Carlo Simulations
摘要：
用解析和数值方法研究了蒙特卡罗模拟中遍历极限的求解方法。借助一个随机模型，定义了一个度量，使检查的模拟在遍历和非遍历制度。在非遍历制度，该模型意味着如何模拟预计接近遍历行为分析，和分析推断的衰减规律的度量允许监测的遍历行为的发生。该度量与先前定义的分子动力学模拟的措施，和度量，使不同的Monte Carlo计划的相对效率的比较。Lennard-Jones 13-粒子簇的应用程序被证明与基于Metropolis，J-步行和并行回火的方法的模型相匹配。这三个Monte Carlo方法的相对效率进行了比较，和衰减规律被证明是有用的，在确定所需的高温参数并行回火和J-行走的原子团簇的研究。
英文摘要：
The approach to the ergodic limit in Monte Carlo simulations is studied using both analytic and numerical methods. With the help of a stochastic model, a metric is defined that enables the examination of a simulation in both the ergodic and non-ergodic regimes. In the non-ergodic regime, the model implies how the simulation is expected to approach ergodic behavior analytically, and the analytically inferred decay law of the metric allows the monitoring of the onset of ergodic behavior. The metric is related to previously defined measures developed for molecular dynamics simulations, and the metric enables the comparison of the relative efficiencies of different Monte Carlo schemes. Applications to Lennard-Jones 13-particle clusters are shown to match the model for Metropolis, J-walking and parallel tempering based approaches. The relative efficiencies of these three Monte Carlo approaches are compared, and the decay law is shown to be useful in determining needed high temperature parameters in parallel tempering and J-walking studies of atomic clusters.
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