Self-Consistent Ornstein-Zernike Approximation for Lattice Gases.

A self-consistent approximation for the structure factor of three-dimensional lattice gases yields remarkably accurate predictions (less than 3{percent} 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{percent}, and other critical properties to within (1{endash}2){percent}, of the best numerical estimates. Until temperature and density are within 1{percent} of their critical values, the approximate {ital 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. {copyright} {ital 1996 The American Physical Society.}