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The hierarchical reference theory (HRT) and the self-consistentOrnstein-Zernike approximation (SCOZA) are two liquid state theories that bothfurnish a largely satisfactory description of the critical region as well asthe phase coexistence and equation of state in general. Furthermore, there area number of similarities that suggest the possibility of a unification of boththeories. Earlier in this respect we have studied consistency between theinternal energy and free energy routes. As a next step toward this goal we hereconsider consistency with the compressibility route too, but we restrictexplicit evaluations to a model whose exact solution is known showing that aunification works in that case. The model in question is the mean sphericalmodel (MSM) which we here extend to a generalized MSM (GMSM). For this case, weshow that the correct solutions can be recovered from suitable boundaryconditions through either of SCOZA or HRT alone as well as by the combinedtheory. Furthermore, the relation between the HRT-SCOZA equations and those ofSCOZA and HRT becomes transparent.Comment: Minimal correction of some typos found during proof reading. Accepted  for publication in Phys. Rev.

physical review. e, statistical, nonlinear and soft matter physics

Towards a unification of hierarchical reference theory and self-consistent Ornstein-Zernike approximation: Analysis of exactly solvable mean-spherical and generalized mean-spherical models