Critical region of D-dimensional spins: extension and analysis of the hierarchical referencetheory

The hierarchical reference theory (HRT) is generalised to spins of dimensionality D. Then its properties are investigated by both analytical and numerical evaluations for supercritical temperatures. The HRT is closely related to the self-consistent Ornstein-Zernike approximation (SCOZA) that was developed earlier for arbitrary D. Like the D = 1 case we studied earlier, our investigation is facilitated by a situation where both HRT and SCOZA give identical results with a mean spherical model behaviour (i.e. D = infinity). However, for the more general situation we find that an additional intermediate term appears. With an interplay between leading and subleading contributions, simple rational numbers, independent of D (<infinity), are found for the critical indices.