流体的光滑截止层次参照理论
The smooth cut-off Hierarchical Reference Theory of fluids
摘要：
我们提供了一个全面的介绍分层参考理论（HRT）的平滑截止制定。一个简单的和自洽的推导的微分方程的层次补充与已知的尖锐的截止HRT的比较。然后，该理论被应用到一个硬核汤川流体（HCYF）：一个封闭，基于平均球近似anomaly，进行了详细的研究，并讨论了其有趣的关系，自洽Ornstein-Zernike近似。研究了在临界点附近的渐近性质，并与临界温度以上和以下的重整化群结果进行了比较。HRT自由能总是密度的凸函数，导致在共存时具有有限压缩性的两相区中的平坦等温线。这使得HRT的唯一的液态理论能够直接获得流体-流体相平衡，而不诉诸麦克斯韦建设。平均场自由能由于包含密度涨落而被修改的方式提示了如何识别旋节曲线。本文研究了HCYF的热力学性质和关联函数，其中反Yukawa范围的三个值为：z=1.8，z=4和z=7，其中蒙特卡罗模拟是可用的。还研究了液-汽临界点相对于冻结的稳定性。
英文摘要：
We provide a comprehensive presentation of the Hierarchical Reference Theory (HRT) in the smooth cut-off formulation. A simple and self-consistent derivation of the hierarchy of differential equations is supplemented by a comparison with the known sharp cut-off HRT. Then, the theory is applied to a hard core Yukawa fluid (HCYF): a closure, based on a mean spherical approximation ansatz, is studied in detail and its intriguing relationship to the self consistent Ornstein-Zernike approximation is discussed. The asymptotic properties, close to the critical point are investigated and compared to the renormalization group results both above and below the critical temperature. The HRT free energy is always a convex function of the density, leading to flat isotherms in the two-phase region with a finite compressibility at coexistence. This makes HRT the sole liquid-state theory able to obtain directly fluid-fluid phase equilibrium without resorting to the Maxwell construction. The way the mean field free energy is modified due to the inclusion of density fluctuations suggests how to identify the spinodal curve. Thermodynamic properties and correlation functions of the HCYF are investigated for three values of the inverse Yukawa range: z=1.8, z=4 and z=7 where Monte Carlo simulations are available. The stability of the liquid-vapor critical point with respect to freezing is also studied.
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