Self-consistent approximation for fluids and lattice gases

A self-consistent Ornstein-Zernike approximation (SCOZA) for the direct-cor relation function, embodying consistency between the compressibility and th e internal energy routes to the thermodynamics, has recently been quantitat ively evaluated for a nearest-neighbor attractive lattice gas and for a flu id of Yukawa spheres, in which the pair potential has a hard core and an at tractive Yukawa tail. For the lattice gas the SCOZA yields remarkably accur ate predictions for the thermodynamics, the correlations, the critical poin t, and the coexistence curve. The critical temperature agrees to within 0.2 % of the best estimates based on extrapolation of series expansions. Until the temperature is to within less than 1 % of its critical value, the effe ctive critical exponents do not differ appreciably from their estimated exa ct form, so that the thermodynamics deviates from the correct behavior only in a very narrow neighborhood of the critical point. For the Yukawa fluid accurate results are obtained as well, although a comparison as sharp as in the lattice-gas case has not been possible due to the greater uncertainty affecting the available simulation results, especially with regard to the p osition of the critical point and the coexistence curve.