Continuous Demixing Transition of Binary Liquids: Finite‐Size Scaling from the Analysis of Sub‐Systems,Advanced Theory and Simulations

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Continuous Demixing Transition of Binary Liquids: Finite‐Size Scaling from the Analysis of Sub‐Systems
Advanced Theory and Simulations ( IF 2.9 ) Pub Date : 2021-01-28 , DOI: 10.1002/adts.202000235
Yogyata Pathania ₁ , Dipanjan Chakraborty ₁ , Felix Höfling _{2,

3}

Affiliation

A binary liquid near its consolute point exhibits critical fluctuations of local composition and a diverging correlation length. The method of choice to calculate critical points in the phase diagram is a finite‐size scaling analysis, based on a sequence of simulations with widely different system sizes. Modern, massively parallel hardware facilitates that instead cubic sub‐systems of one large simulation are used. Here, this alternative is applied to a symmetric binary liquid at critical composition and different routes to the critical temperature are compared: 1) fitting critical divergences of the composition structure factor, 2) scaling of fluctuations in sub‐volumes, and 3) applying the cumulant intersection criterion to sub‐systems. For the last route, two difficulties arise: sub‐volumes are open systems, for which no precise estimate of the critical Binder cumulant

U_{c}

is available. Second, the boundaries of the simulation box interfere with the sub‐volumes, which is resolved here by a two‐parameter finite‐size scaling. The implied modification to the data analysis restores the common intersection point, yielding

U_{c} = 0.201 \pm 0.001

, universal for cubic Ising‐like systems with free boundaries. Confluent corrections to scaling, which arise for small sub‐system sizes, are quantified and the data are compatible with the universal correction exponent

ω \approx 0.83

.

中文翻译：

二元液体的连续混合过渡：子系统分析的有限尺寸比例

接近其固结点的二元液体表现出局部组成的临界波动和相关长度的发散。在相图中计算临界点的选择方法是有限大小的比例分析，该分析基于一系列具有广泛不同系统尺寸的仿真。现代的大规模并行硬件有助于使用一个大型模拟的立方子系统。在这里，此替代方法适用于临界组成的对称二元液体，并比较了到达临界温度的不同途径：1）拟合组成结构因子的临界散度； 2）调整小体积的波动； 3）应用子系统的累积相交标准。对于最后一条路线，出现了两个困难：子卷是开放系统，