Density correlations in lattice gases in contact with a confining wall

A discrete version of classical density functional theory applicable to lattice gases or Ising spin systems is proposed, which accounts for the requirement of particle-hole symmetry in the presence of pairwise forces. Results of our theory for density profiles and two-particle correlation functions in two-dimensional strip geometries compare favorably with Monte Carlo simulations. Some problems with standard "weighted-density" approximation schemes, when applied to lattice gases, are pointed out.