A self-consistent approximation for the structure factor of three-dimensional lattice gases yields remarkably accurate predictions (less than 3% error over most of the temperature range) for the correlation length, isothermal compressibility, specific heat, and the coexistence curve. Critical temperatures agree to within 0.2%, and other critical properties to within (1–2)%, of the best numerical estimates. Until temperature and density are within 1% of their critical values, the approximate effective critical exponents do not differ appreciably from their estimated exact form; they attain their limiting spherical-model values only much closer to critical. The method should prove useful for a variety of three-dimensional lattice-gas and fluid problems; it is inappropriate to two dimensions, where it predicts criticality at zero temperature.

• Received 1 September 1995

DOI:https://doi.org/10.1103/PhysRevLett.77.996