Unification of hierarchical reference theory and self-consistent Ornstein-Zernike approximation: Analysis of the critical region for fluids and lattice gases

The hierarchical reference theory (HRT) and the self-consistent Ornstein-Zernike approximation (SCOZA) are two liquid state theories that both yield a largely satisfactory description of the critical region as well as the phase coexistence and equation of state in general. In two previous works, unification of these theories has been considered and general equations were established. Further it was shown that the solution of the mean spherical model and a generalized version of it can be obtained in this way. In the present work, analysis of the critical region for fluids and lattice gases is performed. A key result of our HRT-SCOZA approximation is that for the standard three-dimensional fluid, lattice gas, or Ising model, the critical index for the critical isotherm is delta=5 and for the curve of coexistence it is beta=1/3 provided full scaling is assumed. More generally we find beta=2/(delta+1).