Self-consistent approximation for fluids and lattice gases

A self-consistent Ornstein-Zernike approximation (SCOZA) for the direct-correlation function, embodying consistency between the compressibility and the internal energy routes to the thermodynamics, has recently been quantitatively evaluated for a nearest-neighbor attractive lattice gas and for a fluid of Yukawa spheres, in which the pair potential has a hard core and an attractive Yukawa tail. For the lattice gas the SCOZA yields remarkably accurate predictions for the thermodynamics, the correlations, the critical point, 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 effective critical exponents do not differ appreciably from their estimated exact 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 position of the critical point and the coexistence curve.