ABSTRACT We address the problem of how to choose the parameters of a Gibbs Ensemble Monte Carlo (GEMC) simulation of phase separation optimally through a systematic study of the autocorrelation functions of density fluctuation in a particular example. In this model the particles interact via a square well potential. Values of the temperature as well as the range of the square well potential are varied. We find that the normalised autocorrelation function is described accurately over a very large time scale as a linear combination of an exponential function with a time scale τ2 and a stretched exponential function with a time scale τ1 and an exponent α. Dependence of α, τ1 and τ2 on the temperature, the parameters of the GEMC algorithm and the range of the square well potential is investigated and interpreted. We use the insight thus obtained and the generality of some aspects of these results to construct the route to optimisation of the parameters of a GEMC simulation in a somewhat more generic situation involving a single-component phase separation.

中文翻译：

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优化Gibbs Ensemble Monte Carlo模拟相分离的参数：多重弛豫时间的作用

摘要 我们通过对特定示例中密度波动的自相关函数的系统研究，解决了如何最佳地选择相分离的吉布斯集合蒙特卡罗 (GEMC) 模拟的参数的问题。在这个模型中，粒子通过方阱势相互作用。温度值以及方阱电位的范围是变化的。我们发现归一化自相关函数在非常大的时间尺度上被准确地描述为时间尺度为 τ2 的指数函数和时间尺度为 τ1 和指数 α 的拉伸指数函数的线性组合。研究和解释了 α、τ1 和 τ2 对温度、GEMC 算法参数和方阱电位范围的依赖性。