Thermodynamically self-consistent theory of structure for three-dimensional lattice gases

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Recently, methods were developed to solve with high accuracy the equations that describe a thermodynamically self-consistent theory for the two-body correlation function, and preliminary results were reported for three-dimensional lattice gases with nearest-neighbor attractive interaction [R. Dickman and G. Stell, Phys. Rev. Lett. 77, 996 (1996)]. Here we give a detailed description of our methods and of the results, which are found to be remarkably accurate for both the thermodynamics and structure of these systems. In particular, critical temperatures are predicted to within 0.2% of the best estimates from series expansions. Although above the critical temperature the theory yields the same critical exponents as the spherical model, this asymptotic behavior sets in only in a very narrow region around the critical point, so that the apparent exponents and the thermodynamics are well reproduced up to reduced temperatures of around ${10}^{\ensuremath{-}2}$. On the coexistence curve, on the other hand, the exponents are nonspherical, and considerably more accurate than the spherical ones. For instance, the exponent ${\ensuremath{\beta}}_{\mathrm{coex}}$ predicted by the theory for the shape of the coexistence curve is ${\ensuremath{\beta}}_{\mathrm{coex}}=0.35$.