Analysis of the critical region of the hierarchical reference theory

作者：Hoye Johan S^*; Lomba Enrique

来源：Molecular Physics, 2011, 109(23-24): 2773-2786.

DOI：10.1080/00268976.2011.627384

• criticality
• integral equations
• Ornstein Zernike
• HRT
• SCOZA

The critical region of the hierarchical reference theory (HRT) is investigated both by analytical and numerical methods. This is closely related to a recent work by one of us where the HRT was unified with another accurate theory, the self-consistent Ornstein-Zernike theory (SCOZA). It was found that somehow the properties of HRT alone would be closely related to the critical properties of the unified problem and vice versa. Our investigation is facilitated by the discovery of a situation where HRT and SCOZA give identical results. For the more general HRT situation we then find that an additional intermediate term appears, and the generalized scaling of SCOZA is replaced with standard scaling. Further we find that the numerical results can be accurately expressed by simple analytic expressions in the critical region. With an interplay between the leading scaling function and subleading contributions, simple rational numbers are found for the critical indices.

• 出版日期2011