Critical properties of the hierarchical reference theory

TL;DR

This paper investigates the critical properties of the hierarchical reference theory (HRT) directly through its differential equations, confirming that its critical indices in three dimensions are simple rational numbers.

Contribution

The study provides a direct analysis of HRT's critical behavior, extending previous indirect methods and establishing simple rational critical indices in three dimensions.

Findings

HRT critical indices are simple rational numbers in 3D

Direct analysis of HRT PDEs confirms previous indirect results

Subleading scaling contributions are characterized by derived ODEs

Abstract

The critical region of the hierarchical reference theory (HRT) is investigated further. This extends an earlier work by us where the critical properties of the HRT were concluded indirectly via another accurate but somewhat different theory, the self-consistent Ornstein-Zernike approximation (SCOZA), and numerical work. In the present work we perform our analysis directly upon the HRT partial differential equation to establish ordinary differential equations for the subleading scaling contributions. Again we find that the HRT critical indices in three dimensions are simple rational numbers.