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Abstract
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.
Acknowledgements
E.L. gratefully acknowledges the support from the Dirección General de Investigación Científica y Técnica under Grant No. FIS2010-15502 and from the Dirección General de Universidades e Investigación de la Comunidad de Madrid under Grant No. S2009/ESP/1691 and Program MODELICO-CM. E.L. also acknowledges the support and hospitality of the Institutt for Fysikk (NTNU), where part of the work was conceived.