2009/01/14 by Alberto Parola, Davide Pini, L. Reatto +1
Engineering · Materials Science · Mathematics · Physics and Astronomy · #Ansatz #Binodal #Compressibility #Critical point (mathematics) #Material Dynamics and Properties #Mathematical analysis #Mathematical physics #Mathematics #Mean field theory #Monte Carlo method #Phase (matter) #Phase Equilibria and Thermodynamics #Phase diagram #Physics #Quantum mechanics #Renormalization group #Spinodal #Statistical physics #Theoretical and Computational Physics #Thermodynamics #Yukawa potential #cond-mat.soft #cond-mat.stat-mech
paper · pdf · doi:10.1080/00268970902873547
23 pages, 15 figures, 1 table
arxiv created 2009/01/14 · openalex publication_date 2009/02/20 · arxiv updated 2015/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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. The theory is then 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 with 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 fluid–fluid phase equilibrium in homogeneous systems 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.